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237 relations: Aaron D. Wyner, Abstract algebra, Alan Tucker, Alex F. T. W. Rosenberg, Alexander Vardy, Algebraic combinatorics, All one polynomial, Alternant code, Alternant matrix, Amin Shokrollahi, Andrew M. Gleason, Andries Brouwer, Arbitrarily varying channel, Arnaldo Garcia, Association scheme, Baum–Welch algorithm, BCH code, Bell Labs, Bent function, Binary erasure channel, Binary symmetric channel, Bipartite graph, Blackwell channel, Block code, Broadcast television systems, Burst error-correcting code, Change of base, Chris Freiling, Cochin University of Science and Technology, Code (disambiguation), Coding gain, Coding theory approaches to nucleic acid design, Coding tree unit, Combinatorics, Computer scientist, Concatenated error correction code, Constant-weight code, Coset leader, Covering code, Cyclic code, Data compression, Data transmission, Dave Forney, David A. Huffman, David Slepian, David Zuckerman (computer scientist), Decoding methods, Deletion channel, Delone set, Digit sum, ..., Discrete Fourier transform (general), Discrete mathematics, Distance, Distance matrix, Distributed source coding, Dominique Perrin, Dual code, Ed Posner, Edgar Gilbert, Ehrhart polynomial, Elias Bassalygo bound, Elwyn Berlekamp, Enumerator polynomial, Erasure code, Eric Lander, Error correction code, Error detection and correction, Error-correcting codes with feedback, Eugene Prange, Eurobalise, Expander code, Extended Euclidean algorithm, Factorization of polynomials over finite fields, Fast syndrome-based hash, Field (mathematics), Filter bank, Finite field, Finite field arithmetic, Folded Reed–Solomon code, Forney algorithm, Forward error correction, Fountain code, Frobenius algebra, Gábor Korchmáros, Generalized minimum-distance decoding, Generator matrix, Gerhard Frey, Gerrit Lekkerkerker, Gilbert–Varshamov bound, Glossary of computer science, Graduate Texts in Mathematics, Griesmer bound, Group (mathematics), Group code, Guruswami–Sudan list decoding algorithm, GV-linear-code, Hadamard code, Hamming bound, Hamming code, Hamming distance, Hamming scheme, Hamming space, Hamming weight, Hamming(7,4), Harold Pender Award, Harriet Pollatsek, Hat puzzle, Heide Gluesing-Luerssen, Hexacode, Hideki Imai, History of geometry, IEEE Transactions on Information Theory, Indian Statistical Institute, Information theory, International Conference on Information Processing in Sensor Networks, Inversion encoding, Iran Workshop on Communication and Information Theory, Irving S. Reed, Italo Jose Dejter, J. H. van Lint, Jack Wolf, James Massey, Jan Kratochvíl, Jessie MacWilliams, Joachim Hagenauer, John Cioffi, John Horton Conway, John Wozencraft, Johnson bound, Judy L. Walker, Justesen code, Kraft–McMillan inequality, Kullback–Leibler divergence, Lattice (group), Lee distance, Leech lattice, Leonard Schulman, Linear code, Linear programming decoding, List decoding, List of academic fields, List of African-American inventors and scientists, List of algebraic coding theory topics, List of Columbia University alumni, List of Columbia University alumni and attendees, List of computer algebra systems, List of computer scientists, List of Dutch inventions and discoveries, List of IEEE awards, List of mathematical theories, List of matrices, List of people from South Orange, New Jersey, List of Queens College people, List of theorems, List of University of Maryland, Baltimore County people, Long code (mathematics), Magma (computer algebra system), Mark Semenovich Pinsker, Marshall Hall (mathematician), Mary Flahive, Matrix (mathematics), Matroid, Michael Luby, Modular representation theory, Mohammad Reza Aref, Moti Yung, Navin M. Singhi, Near-field communication, Nearest neighbor search, Nikil Jayant, Noisy channel model, Non-integer representation, Norm (mathematics), Nucleic acid design, Orthogonal array, Outline of academic disciplines, Outline of combinatorics, Outline of computer science, Outline of discrete mathematics, Outline of science, Parity-check matrix, Peter Cameron (mathematician), Peter Elias, Peter Landrock, PHY (chip), Plotkin bound, Polynomial code, Preparata code, Prior probability, Puncturing, Quantum computing, Raj Chandra Bose, Randall Dougherty, Random permutation, Rank error-correcting code, Reihaneh Safavi-Naini, René Schoof, Repetition code, Representation theory, Richard Blahut, Robert Calderbank, Robert Dorfman, Rom Varshamov, Ronald de Wolf, Roy Adler, SampTA, Sardinas–Patterson algorithm, Self-synchronizing code, Singleton bound, Singly and doubly even, Snake-in-the-box, Solomon W. Golomb, Spherical code, Srivastava code, Standard array, Statistical inference, Systematic code, Tamás Szőnyi, Tanner graph, Ternary Golay code, Theoretical computer science, Theory, Thomas Zaslavsky, Triangular network coding, Underdetermined system, Variable-length code, Vámos matroid, Vector fields on spheres, Vera Pless, Volume of an n-ball, Weissman score, Welch bounds, Winnie Li, Wozencraft ensemble, Z-channel (information theory), Zemor's decoding algorithm, Zigzag code. Expand index (187 more) »
Aaron D. Wyner
Dr.
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Abstract algebra
In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures.
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Alan Tucker
Alan Curtiss Tucker is an American mathematician.
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Alex F. T. W. Rosenberg
Alex F. T. W. Rosenberg (1926–2007) was a German-American mathematician who served as the editor of the Proceedings of the American Mathematical Society from 1960 to 1965, and of the American Mathematical Monthly from 1974 to 1976.
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Alexander Vardy
Alexander Vardy is a Russian-born and Israeli-educated electrical engineer known for his expertise in coding theory.
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Algebraic combinatorics
Algebraic combinatorics is an area of mathematics that employs methods of abstract algebra, notably group theory and representation theory, in various combinatorial contexts and, conversely, applies combinatorial techniques to problems in algebra.
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All one polynomial
An all one polynomial (AOP) is a polynomial in which all coefficients are one.
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Alternant code
In coding theory, alternant codes form a class of parameterised error-correcting codes which generalise the BCH codes.
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Alternant matrix
In linear algebra, an alternant matrix is a matrix with a particular structure, in which successive columns have a particular function applied to their entries.
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Amin Shokrollahi
Amin Shokrollahi (born 1964) is an Iranian mathematician who has worked on a variety of topics including coding theory and algebraic complexity theory.
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Andrew M. Gleason
Andrew Mattei Gleason (19212008) was an American mathematician who as a young World War II naval officer broke German and Japanese military codes, then over the succeeding sixty years made fundamental contributions to widely varied areas of mathematics, including the solution of Hilbert's fifth problem, and was a leader in reform and innovation in teaching at all levels.
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Andries Brouwer
Andries Evert Brouwer (born 1951) is a Dutch mathematician and computer programmer, Professor Emeritus at Eindhoven University of Technology (TU/e).
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Arbitrarily varying channel
An arbitrarily varying channel (AVC) is a communication channel model used in coding theory, and was first introduced by Blackwell, Breiman, and Thomasian.
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Arnaldo Garcia
Arnaldo Leite Pinto Garcia (b. 1950) is a Brazilian mathematician working on algebraic geometry and coding theory.
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Association scheme
The theory of association schemes arose in statistics, in the theory of experimental design for the analysis of variance.
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Baum–Welch algorithm
In electrical engineering, computer science, statistical computing and bioinformatics, the Baum–Welch algorithm is used to find the unknown parameters of a hidden Markov model (HMM).
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BCH code
In coding theory, the BCH codes or Bose–Chaudhuri–Hocquenghem codes form a class of cyclic error-correcting codes that are constructed using polynomials over a finite field (also called Galois field).
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Bell Labs
Nokia Bell Labs (formerly named AT&T Bell Laboratories, Bell Telephone Laboratories and Bell Labs) is an American research and scientific development company, owned by Finnish company Nokia.
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Bent function
In the mathematical field of combinatorics, a bent function is a special type of Boolean function.
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Binary erasure channel
disambiguation: Landauer's principle A binary erasure channel (or BEC) is a common communications channel model used in coding theory and information theory.
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Binary symmetric channel
A binary symmetric channel (or BSC) is a common communications channel model used in coding theory and information theory.
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Bipartite graph
In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets U and V such that every edge connects a vertex in U to one in V. Vertex sets U and V are usually called the parts of the graph.
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Blackwell channel
The Blackwell channel is a deterministic broadcast channel model used in coding theory and information theory.
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Block code
In coding theory, a block code is any member of the large and important family of error-correcting codes that encode data in blocks.
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Broadcast television systems
Broadcast television systems are encoding or formatting standards for the transmission and reception of terrestrial television signals.
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Burst error-correcting code
In coding theory, burst error-correcting codes employ methods of correcting burst errors, which are errors that occur in many consecutive bits rather than occurring in bits independently of each other.
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Change of base
In mathematics, change of base can mean any of several things.
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Chris Freiling
Christopher Francis Freiling is a mathematician responsible for Freiling's axiom of symmetry in set theory.
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Cochin University of Science and Technology
Cochin University of Science and Technology (CUSAT) is a government-owned autonomous science and technology university in Kochi, Kerala, India.
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Code (disambiguation)
A code is a rule for converting a piece of information into another object or action, not necessarily of the same sort.
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Coding gain
In coding theory and related engineering problems, coding gain is the measure in the difference between the signal-to-noise ratio (SNR) levels between the uncoded system and coded system required to reach the same bit error rate (BER) levels when used with the error correcting code (ECC).
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Coding theory approaches to nucleic acid design
DNA code construction refers to the application of coding theory to the design of nucleic acid systems for the field of DNA–based computation.
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Coding tree unit
Coding tree unit (CTU) is the basic processing unit of the High Efficiency Video Coding (HEVC) video standard and conceptually corresponds in structure to macroblock units that were used in several previous video standards.
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Combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures.
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Computer scientist
A computer scientist is a person who has acquired the knowledge of computer science, the study of the theoretical foundations of information and computation and their application.
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Concatenated error correction code
In coding theory, concatenated codes form a class of error-correcting codes that are derived by combining an inner code and an outer code.
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Constant-weight code
In coding theory, a constant-weight code, also called an m-of-n code, is an error detection and correction code where all codewords share the same Hamming weight.
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Coset leader
In coding theory, a coset leader is a word of minimum weight in any particular coset - that is, a word with the lowest amount of non-zero entries.
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Covering code
In coding theory, a covering code is a set of elements (called codewords) in a space, with the property that every element of the space is within a fixed distance of some codeword.
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Cyclic code
In coding theory, a cyclic code is a block code, where the circular shifts of each codeword gives another word that belongs to the code.
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Data compression
In signal processing, data compression, source coding, or bit-rate reduction involves encoding information using fewer bits than the original representation.
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Data transmission
Data transmission (also data communication or digital communications) is the transfer of data (a digital bitstream or a digitized analog signal) over a point-to-point or point-to-multipoint communication channel.
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Dave Forney
George David "Dave" Forney, Jr. (born March 6, 1940) is an American electrical engineer who made contributions in telecommunication system theory, specifically in coding theory and information theory.
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David A. Huffman
David Albert Huffman (August 9, 1925 – October 7, 1999) was a pioneer in computer science, known for his Huffman coding.
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David Slepian
David S. Slepian (June 30, 1923 – November 29, 2007) was an American mathematician.
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David Zuckerman (computer scientist)
David Zuckerman is an American theoretical computer scientist whose work concerns randomness in computation.
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Decoding methods
In coding theory, decoding is the process of translating received messages into codewords of a given code.
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Deletion channel
A deletion channel is a communications channel model used in coding theory and information theory.
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Delone set
In the mathematical theory of metric spaces, ε-nets, ε-packings, ε-coverings, uniformly discrete sets, relatively dense sets, and Delone sets (named after Boris Delone) are several closely related definitions of well-spaced sets of points, and the packing radius and covering radius of these sets measure how well-spaced they are.
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Digit sum
In mathematics, the digit sum of a given integer is the sum of all its digits (e.g. the digit sum of 84001 is calculated as 8+4+0+0+1.
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Discrete Fourier transform (general)
In mathematics, the discrete Fourier transform over an arbitrary ring generalizes the discrete Fourier transform of a function whose values are complex numbers.
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Discrete mathematics
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous.
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Distance
Distance is a numerical measurement of how far apart objects are.
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Distance matrix
In mathematics, computer science and especially graph theory, a distance matrix is a square matrix (two-dimensional array) containing the distances, taken pairwise, between the elements of a set.
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Distributed source coding
Distributed source coding (DSC) is an important problem in information theory and communication.
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Dominique Perrin
Dominique Pierre Perrin (b. 1946) is a French mathematician and theoretical computer scientist known for his contributions to coding theory and to combinatorics on words.
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Dual code
In coding theory, the dual code of a linear code is the linear code defined by where is a scalar product.
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Ed Posner
Edward Charles "Ed" Posner (August 10, 1933 – June 15, 1993) was an American information theorist and neural network researcher who became chief technologist at the Jet Propulsion Laboratory and founded the Conference on Neural Information Processing Systems.
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Edgar Gilbert
Edgar Nelson Gilbert (July 25, 1923 – June 15, 2013) was an American mathematician and coding theorist, a longtime researcher at Bell Laboratories whose accomplishments include the Gilbert–Varshamov bound in coding theory, the Gilbert–Elliott model of bursty errors in signal transmission, and the Erdős–Rényi model for random graphs.
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Ehrhart polynomial
In mathematics, an integral polytope has an associated Ehrhart polynomial that encodes the relationship between the volume of a polytope and the number of integer points the polytope contains.
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Elias Bassalygo bound
The Elias-Bassalygo bound is a mathematical limit used in coding theory for error correction during data transmission or communications.
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Elwyn Berlekamp
Elwyn Ralph Berlekamp (born September 6, 1940) is an American mathematician.
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Enumerator polynomial
In coding theory, the weight enumerator polynomial of a binary linear code specifies the number of words of each possible Hamming weight.
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Erasure code
In coding theory, an erasure code is a forward error correction (FEC) code under the assumption of bit erasures (rather than bit errors), which transforms a message of k symbols into a longer message (code word) with n symbols such that the original message can be recovered from a subset of the n symbols.
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Eric Lander
Eric Steven Lander (born February 3, 1957), a mathematician and geneticist, is a Professor of Biology at the Massachusetts Institute of Technology (MIT), former member of the Whitehead Institute, and founding director of the Broad Institute of MIT and Harvard.
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Error correction code
In computing, telecommunication, information theory, and coding theory, an error correction code, sometimes error correcting code, (ECC) is used for controlling errors in data over unreliable or noisy communication channels.
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Error detection and correction
In information theory and coding theory with applications in computer science and telecommunication, error detection and correction or error control are techniques that enable reliable delivery of digital data over unreliable communication channels.
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Error-correcting codes with feedback
In mathematics, computer science, telecommunication, information theory, and searching theory, error-correcting codes with feedback refers to error correcting codes designed to work in the presence of feedback from the receiver to the sender.
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Eugene Prange
Eugene A. Prange (c. 1918 – February 12, 2006) at legacy.com, accessed 2013-05-05.
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Eurobalise
An Eurobalise is a specific variant of a balise being a transponder placed between the rails of a railway.
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Expander code
In coding theory, expander codes form a class of error-correcting codes that are constructed from bipartite expander graphs.
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Extended Euclidean algorithm
In arithmetic and computer programming, the extended Euclidean algorithm is an extension to the Euclidean algorithm, and computes, in addition to the greatest common divisor of integers a and b, also the coefficients of Bézout's identity, which are integers x and y such that This is a certifying algorithm, because the gcd is the only number that can simultaneously satisfy this equation and divide the inputs.
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Factorization of polynomials over finite fields
In mathematics and computer algebra the factorization of a polynomial consists of decomposing it into a product of irreducible factors.
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Fast syndrome-based hash
In cryptography, the fast syndrome-based hash functions (FSB) are a family of cryptographic hash functions introduced in 2003 by Daniel Augot, Matthieu Finiasz, and Nicolas Sendrier.
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Field (mathematics)
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.
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Filter bank
In signal processing, a filter bank is an array of band-pass filters that separates the input signal into multiple components, each one carrying a single frequency sub-band of the original signal.
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Finite field
In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements.
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Finite field arithmetic
In mathematics, finite field arithmetic is arithmetic in a finite field (a field containing a finite number of elements) as opposed to arithmetic in a field with an infinite number of elements, like the field of rational numbers.
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Folded Reed–Solomon code
In coding theory, folded Reed–Solomon codes are like Reed–Solomon codes, which are obtained by mapping m Reed–Solomon codewords over a larger alphabet by careful bundling of codeword symbols.
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Forney algorithm
In coding theory, the Forney algorithm (or Forney's algorithm) calculates the error values at known error locations.
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Forward error correction
In telecommunication, information theory, and coding theory, forward error correction (FEC) or channel coding is a technique used for controlling errors in data transmission over unreliable or noisy communication channels.
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Fountain code
In coding theory, fountain codes (also known as rateless erasure codes) are a class of erasure codes with the property that a potentially limitless sequence of encoding symbols can be generated from a given set of source symbols such that the original source symbols can ideally be recovered from any subset of the encoding symbols of size equal to or only slightly larger than the number of source symbols.
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Frobenius algebra
In mathematics, especially in the fields of representation theory and module theory, a Frobenius algebra is a finite-dimensional unital associative algebra with a special kind of bilinear form which gives the algebras particularly nice duality theories.
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Gábor Korchmáros
Gábor Korchmáros (born 1948) is a Hungarian mathematician, who works on finite geometry.
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Generalized minimum-distance decoding
In coding theory, generalized minimum-distance (GMD) decoding provides an efficient algorithm for decoding concatenated codes, which is based on using an errors-and-erasures decoder for the outer code.
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Generator matrix
In coding theory, a generator matrix is a matrix whose rows form a basis for a linear code.
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Gerhard Frey
Gerhard Frey (born 1944) is a German mathematician, known for his work in number theory.
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Gerrit Lekkerkerker
Cornelis Gerrit Lekkerkerker (Harmelen, 7 February 1922 – 24 July 1999) was a Dutch mathematician.
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Gilbert–Varshamov bound
In coding theory, the Gilbert–Varshamov bound (due to Edgar Gilbert and independently Rom Varshamov) is a limit on the parameters of a (not necessarily linear) code.
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Glossary of computer science
Most of the terms listed in Wikipedia glossaries are already defined and explained within Wikipedia itself.
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Graduate Texts in Mathematics
Graduate Texts in Mathematics (GTM) (ISSN 0072-5285) is a series of graduate-level textbooks in mathematics published by Springer-Verlag.
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Griesmer bound
In the mathematics of coding theory, the Griesmer bound, named after James Hugo Griesmer, is a bound on the length of linear binary codes of dimension k and minimum distance d. There is also a very similar version for non-binary codes.
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Group (mathematics)
In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.
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Group code
In coding theory, group codes are a type of code.
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Guruswami–Sudan list decoding algorithm
In coding theory, list decoding is an alternative to unique decoding of error-correcting codes for large error rates.
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GV-linear-code
In coding theory, the bound of parameters such as rate R, relative distance, block length, etc.
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Hadamard code
The Hadamard code is an error-correcting code named after Jacques Hadamard that is used for error detection and correction when transmitting messages over very noisy or unreliable channels.
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Hamming bound
In mathematics and computer science, in the field of coding theory, the Hamming bound is a limit on the parameters of an arbitrary block code: it is also known as the sphere-packing bound or the volume bound from an interpretation in terms of packing balls in the Hamming metric into the space of all possible words.
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Hamming code
In telecommunication, Hamming codes are a family of linear error-correcting codes.
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Hamming distance
In information theory, the Hamming distance between two strings of equal length is the number of positions at which the corresponding symbols are different.
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Hamming scheme
The Hamming scheme, named after Richard Hamming, is also known as the hyper-cubic association scheme, and it is the most important example for coding theory.
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Hamming space
In statistics and coding theory, a Hamming space is usually the set of all 2^N binary strings of length N. It is used in the theory of coding signals and transmission.
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Hamming weight
The Hamming weight of a string is the number of symbols that are different from the zero-symbol of the alphabet used.
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Hamming(7,4)
In coding theory, Hamming(7,4) is a linear error-correcting code that encodes four bits of data into seven bits by adding three parity bits.
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Harold Pender Award
The Harold Pender Award, initiated in 1972 and named after founding Dean Harold Pender, is given by the Faculty of the School of Engineering and Applied Science of the University of Pennsylvania to an outstanding member of the engineering profession who has achieved distinction by significant contributions to society.
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Harriet Pollatsek
Harriet Suzanne Katcher Pollatsek (born Harriet Katcher in May 2, 1942) is an American mathematician and Professor Emeritus of Mathematics at Mount Holyoke College.
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Hat puzzle
Hat puzzles are logic problems that date back to as early as 1961.
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Heide Gluesing-Luerssen
Heide Gluesing-Luerssen is a German mathematician specializing in algebraic coding theory.
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Hexacode
In coding theory, the hexacode is a length 6 linear code of dimension 3 over the Galois field GF(4).
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Hideki Imai
is an information theorist and cryptographer, currently the director of Research Center for Information Security (RCIS), National Institute of Advanced Industrial Science and Technology (AIST) and a full professor at Chuo University.
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History of geometry
Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") arose as the field of knowledge dealing with spatial relationships.
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IEEE Transactions on Information Theory
IEEE Transactions on Information Theory is a monthly peer-reviewed scientific journal published by the IEEE Information Theory Society.
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Indian Statistical Institute
Indian Statistical Institute (ISI) is an academic institute of national importance as recognised by a 1959 act of the Indian parliament.
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Information theory
Information theory studies the quantification, storage, and communication of information.
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International Conference on Information Processing in Sensor Networks
IPSN, the IEEE/ACM International Conference on Information Processing in Sensor Networks, is an academic conference on sensor networks with its main focus on information processing aspects of sensor networks.
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Inversion encoding
Inversion Encoding is an encoding technique used for encoding bus transmissions for low power systems.
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Iran Workshop on Communication and Information Theory
The Iran Workshop on Communication and Information Theory (IWCIT) (کارگاه ملی نظریه اطلاعات و مخابرات.) is an international academic workshop that is held annually in one of the Iranian University campuses.
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Irving S. Reed
Irving Stoy Reed (November 12, 1923 – September 11, 2012) was a mathematician and engineer.
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Italo Jose Dejter
Italo Jose Dejter (Bahia Blanca, December 17, 1939) is an Argentine-born American mathematician and a retired professor of Mathematics and Computer Science at the University of Puerto Rico (UPRRP), active in that location from August 1984 to February 2018.
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J. H. van Lint
Jacobus Hendricus ("Jack") van Lint (1 September 1932 – 28 September 2004) was a Dutch mathematician, professor at the Eindhoven University of Technology, of which he was rector magnificus from 1991 till 1996.
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Jack Wolf
Jack Keil Wolf (March 14, 1935 – May 12, 2011) was an American researcher in information theory and coding theory.
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James Massey
James Lee Massey (February 11, 1934 – June 16, 2013) was an information theorist and cryptographer, Professor Emeritus of Digital Technology at ETH Zurich.
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Jan Kratochvíl
Jan Kratochvíl (born 10 February 1959) is a Czech mathematician and computer scientist whose research concerns graph theory and intersection graphs.
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Jessie MacWilliams
Florence Jessie MacWilliams (4 January 1917 – 27 May 1990) was an English mathematician who contributed to the field of coding theory.
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Joachim Hagenauer
Joachim Hagenauer (born 29 July 1941) is an information theorist and professor emeritus at Technical University of Munich.
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John Cioffi
John Cioffi (born November 7, 1956) is an American electrical engineer, educator and prolific inventor who has made contributions in telecommunication system theory, specifically in coding theory and information theory.
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John Horton Conway
John Horton Conway FRS (born 26 December 1937) is an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory.
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John Wozencraft
John McReynolds "Jack" Wozencraft (September 30, 1925 – August 31, 2009) was an electrical engineer and information theorist, professor emeritus at the Massachusetts Institute of Technology.
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Johnson bound
In applied mathematics, the Johnson bound (named after Selmer Martin Johnson) is a limit on the size of error-correcting codes, as used in coding theory for data transmission or communications.
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Judy L. Walker
Judy Leavitt Walker is an American mathematician.
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Justesen code
In coding theory, Justesen codes form a class of error-correcting codes that have a constant rate, constant relative distance, and a constant alphabet size.
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Kraft–McMillan inequality
In coding theory, the Kraft–McMillan inequality gives a necessary and sufficient condition for the existence of a prefix code (in Leon G. Kraft's version) or a uniquely decodable code (in Brockway McMillan's version) for a given set of codeword lengths.
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Kullback–Leibler divergence
In mathematical statistics, the Kullback–Leibler divergence (also called relative entropy) is a measure of how one probability distribution diverges from a second, expected probability distribution.
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Lattice (group)
In geometry and group theory, a lattice in \mathbbR^n is a subgroup of the additive group \mathbb^n which is isomorphic to the additive group \mathbbZ^n, and which spans the real vector space \mathbb^n.
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Lee distance
In coding theory, the Lee distance is a distance between two strings x_1 x_2 \dots x_n and y_1 y_2 \dots y_n of equal length n over the q-ary alphabet of size q ≥ 2.
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Leech lattice
In mathematics, the Leech lattice is an even unimodular lattice Λ24 in 24-dimensional Euclidean space, which is one of the best models for the kissing number problem.
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Leonard Schulman
Leonard J. Y. Schulman (born September 14, 1963) is Professor of Computer Science in the Computing and Mathematical Sciences Department at the California Institute of Technology.
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Linear code
In coding theory, a linear code is an error-correcting code for which any linear combination of codewords is also a codeword.
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Linear programming decoding
In information theory and coding theory, linear programming decoding (LP decoding) is a decoding method which uses concepts from linear programming (LP) theory to solve decoding problems.
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List decoding
In computer science, particularly in coding theory, list decoding is an alternative to unique decoding of error-correcting codes for large error rates.
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List of academic fields
The following outline is provided as an overview of an topical guide to academic disciplines: An academic discipline or field of study is known as a branch of knowledge.
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List of African-American inventors and scientists
This list of black inventors and scientists documents many of the African Americans who have invented a multitude of items or made discoveries in the course of their lives.
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List of algebraic coding theory topics
This is a list of algebraic coding theory topics.
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List of Columbia University alumni
This is a sorted list of notable persons who are alumni of Columbia University, New York City.
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List of Columbia University alumni and attendees
This is a partial list of notable persons who have had ties to Columbia University.
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List of computer algebra systems
The following tables provide a comparison of computer algebra systems (CAS).
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List of computer scientists
This is a list of computer scientists, people who do work in computer science, in particular researchers and authors.
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List of Dutch inventions and discoveries
The Netherlands had a considerable part in the making of modern society.
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List of IEEE awards
Through its awards program, the Institute of Electrical and Electronics Engineers recognizes contributions that advance the fields of interest to the IEEE.
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List of mathematical theories
This is a list of mathematical theories.
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List of matrices
This page lists some important classes of matrices used in mathematics, science and engineering.
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List of people from South Orange, New Jersey
Notable current and former residents of South Orange, New Jersey include.
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List of Queens College people
This is a list of notable alumni and faculty of Queens College, City University of New York.
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List of theorems
This is a list of theorems, by Wikipedia page.
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List of University of Maryland, Baltimore County people
No description.
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Long code (mathematics)
In theoretical computer science and coding theory, the long code is an error-correcting code that is locally decodable.
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Magma (computer algebra system)
Magma is a computer algebra system designed to solve problems in algebra, number theory, geometry and combinatorics.
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Mark Semenovich Pinsker
Mark Semenovich Pinsker (Марк Семено́вич Пи́нскер; April 24, 1925 – December 23, 2003) or Mark Shlemovich Pinsker (Марк Шлемо́вич Пи́нскер) was a noted Russian mathematician in the fields of information theory, probability theory, coding theory, ergodic theory, mathematical statistics, and communication networks.
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Marshall Hall (mathematician)
Marshall Hall, Jr. (17 September 1910 – 4 July 1990) was an American mathematician who made significant contributions to group theory and combinatorics.
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Mary Flahive
Mary Elizabeth Flahive (born 1948) is a professor of mathematics at Oregon State University.
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Matrix (mathematics)
In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.
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Matroid
In combinatorics, a branch of mathematics, a matroid is a structure that abstracts and generalizes the notion of linear independence in vector spaces.
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Michael Luby
Michael George Luby is a mathematician and computer scientist, VP Technology at Qualcomm, co-founder and former Chief Technology Officer of Digital Fountain.
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Modular representation theory
Modular representation theory is a branch of mathematics, and that part of representation theory that studies linear representations of finite groups over a field K of positive characteristic.
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Mohammad Reza Aref
Mohammad Reza Aref (محمدرضا عارف, born 19 December 1951) is an Iranian engineer, academic and reformist politician who is currently parliamentary leader of reformists' Hope fraction in the Iranian Parliament, representing Tehran, Rey, Shemiranat and Eslamshahr.
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Moti Yung
Mordechai M. (Moti) Yung is an Israeli-American cryptographer and computer scientist with an extensive industrial research career.
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Navin M. Singhi
Navin Madhavprasad Singhi (born 1949) is an Indian mathematician and a professor at Tata Institute of Fundamental Research Mumbai, specializing in combinatorics and graph theory.
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Near-field communication
Near-field communication (NFC) is a set of communication protocols that enable two electronic devices, one of which is usually a portable device such as a smartphone, to establish communication by bringing them within 4 cm (1.6 in) of each other.
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Nearest neighbor search
Nearest neighbor search (NNS), as a form of proximity search, is the optimization problem of finding the point in a given set that is closest (or most similar) to a given point.
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Nikil Jayant
Nikil Jayant (1945 --) is a prominent communications engineer who was a long-term researcher at Bell Laboratories and subsequently a professor at Georgia Institute of Technology.
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Noisy channel model
The noisy channel model is a framework used in spell checkers, question answering, speech recognition, and machine translation.
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Non-integer representation
A non-integer representation uses non-integer numbers as the radix, or bases, of a positional numbering system.
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Norm (mathematics)
In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero.
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Nucleic acid design
Nucleic acid design is the process of generating a set of nucleic acid base sequences that will associate into a desired conformation.
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Orthogonal array
In mathematics, in the area of combinatorial designs, an orthogonal array is a "table" (array) whose entries come from a fixed finite set of symbols (typically), arranged in such a way that there is an integer t so that for every selection of t columns of the table, all ordered t-tuples of the symbols, formed by taking the entries in each row restricted to these columns, appear the same number of times.
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Outline of academic disciplines
An academic discipline or field of study is a branch of knowledge that is taught and researched as part of higher education.
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Outline of combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures.
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Outline of computer science
Computer science (also called computing science) is the study of the theoretical foundations of information and computation and their implementation and application in computer systems.
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Outline of discrete mathematics
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous.
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Outline of science
The following outline is provided as a topical overview of science: Science – the systematic effort of acquiring knowledge—through observation and experimentation coupled with logic and reasoning to find out what can be proved or not proved—and the knowledge thus acquired.
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Parity-check matrix
In coding theory, a parity-check matrix of a linear block code C is a matrix which describes the linear relations that the components of a codeword must satisfy.
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Peter Cameron (mathematician)
Peter Jephson Cameron FRSE (born 23 January 1947) is an Australian mathematician who works in group theory, combinatorics, coding theory, and model theory.
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Peter Elias
Peter Elias (November 23, 1923 – December 7, 2001) was a pioneer in the field of information theory.
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Peter Landrock
Peter Landrock (born August 20, 1948 in Horsens) is a Danish cryptographer and mathematician.
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PHY (chip)
PHY is an abbreviation for the physical layer of the OSI model and refers to the circuitry required to implement physical layer functions.
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Plotkin bound
In the mathematics of coding theory, the Plotkin bound, named after Morris Plotkin, is a limit (or bound) on the maximum possible number of codewords in binary codes of given length n and given minimum distance d.
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Polynomial code
In coding theory, a polynomial code is a type of linear code whose set of valid code words consists of those polynomials (usually of some fixed length) that are divisible by a given fixed polynomial (of shorter length, called the generator polynomial).
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Preparata code
In coding theory, the Preparata codes form a class of non-linear double-error-correcting codes.
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Prior probability
In Bayesian statistical inference, a prior probability distribution, often simply called the prior, of an uncertain quantity is the probability distribution that would express one's beliefs about this quantity before some evidence is taken into account.
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Puncturing
In coding theory, puncturing is the process of removing some of the parity bits after encoding with an error-correction code.
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Quantum computing
Quantum computing is computing using quantum-mechanical phenomena, such as superposition and entanglement.
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Raj Chandra Bose
Raj Chandra Bose (19 June 1901 – 31 October 1987) was an Indian American mathematician and statistician best known for his work in design theory, finite geometry and the theory of error-correcting codes in which the class of BCH codes is partly named after him.
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Randall Dougherty
Randall Dougherty (born 1961) is an American mathematician.
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Random permutation
A random permutation is a random ordering of a set of objects, that is, a permutation-valued random variable.
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Rank error-correcting code
In coding theory, rank codes (also called Gabidulin codes) are non-binaryCodes for which each input symbol is from a set of size greater than 2.
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Reihaneh Safavi-Naini
Reihaneh (Rei) Safavi-Naini (ريحانه صفوی نائينی) is the AITF Strategic Chair in Information Security at the University of Calgary, Canada.
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René Schoof
René Schoof (born 8 May 1955, Den Helder) at the University of Amsterdam Album Academicum website is a mathematician from the Netherlands who works in Algebraic Number Theory, Arithmetic Algebraic Geometry, Computational Number Theory and Coding Theory.
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Repetition code
In coding theory, the repetition code is one of the most basic error-correcting codes.
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Representation theory
Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures.
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Richard Blahut
Richard Blahut, as a member of National Academy of Engineering in Electronics, Communication & Information Systems Engineering and Computer Science & Engineering for pioneering work in coherent emitter signal processing and for contributions to information theory and error control codes.
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Robert Calderbank
Robert Calderbank (born 28 December 1954) is a professor of Computer Science, Electrical Engineering, and Mathematics and director of the Information Initiative at Duke.
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Robert Dorfman
Robert Dorfman (27 October 1916 – 24 June 2002) was emeritus professor of political economy at Harvard University.
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Rom Varshamov
Rom Rubenovich Varshamov (Russian Ром Рубенович Варшамов; Born April 9, 1927 in Tbilisi; Died August 24, 1999 in Moscow) was a Soviet Armenian mathematician who worked in Coding theory, especially on error-correcting codes and Number theory.
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Ronald de Wolf
Ronald de Wolf is a Dutch Computer Scientist, currently a Senior Researcher at Centrum Wiskunde & Informatica (CWI) and a Professor at the Institute for Logic, Language and Computation (ILLC) of the University of Amsterdam (UvA).
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Roy Adler
Roy Lee Adler (February 22, 1931 – July 26, 2016) was an American mathematician.
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SampTA
SampTA (Sampling Theory and Applications) is a biennial interdisciplinary conference for mathematicians, engineers, and applied scientists.
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Sardinas–Patterson algorithm
In coding theory, the Sardinas–Patterson algorithm is a classical algorithm for determining in polynomial time whether a given variable-length code is uniquely decodable, named after August Albert Sardinas and George W. Patterson, who published it in 1953.
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Self-synchronizing code
In coding theory, especially in telecommunications, a self-synchronizing code is a uniquely decodable code in which the symbol stream formed by a portion of one code word, or by the overlapped portion of any two adjacent code words, is not a valid code word.
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Singleton bound
In coding theory, the Singleton bound, named after Richard Collom Singleton, is a relatively crude upper bound on the size of an arbitrary block code C with block length n, size M and minimum distance d.
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Singly and doubly even
In mathematics an even integer, that is, a number that is divisible by 2, is called evenly even or doubly even if it is a multiple of 4, and oddly even or singly even if it is not.
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Snake-in-the-box
The snake-in-the-box problem in graph theory and computer science deals with finding a certain kind of path along the edges of a hypercube.
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Solomon W. Golomb
Solomon Wolf Golomb (May 30, 1932 – May 1, 2016) was an American mathematician, engineer, and professor of electrical engineering at the University of Southern California, best known for his works on mathematical games.
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Spherical code
In geometry and coding theory, a spherical code with parameters (n,N,t) is a set of N points on the unit hypersphere in n dimensions for which the dot product of unit vectors from the origin to any two points is less than or equal to t. The kissing number problem may be stated as the problem of finding the maximal N for a given n for which a spherical code with parameters (n,N,1/2) exists.
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Srivastava code
In coding theory, Srivastava codes, formulated by Professor J. N. Srivastava, form a class of parameterised error-correcting codes which are a special case of alternant codes.
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Standard array
In coding theory, a standard array (or Slepian array) is a q^ by q^ array that lists all elements of a particular \mathbb_q^n vector space.
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Statistical inference
Statistical inference is the process of using data analysis to deduce properties of an underlying probability distribution.
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Systematic code
In coding theory, a systematic code is any error-correcting code in which the input data is embedded in the encoded output.
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Tamás Szőnyi
Tamás Szőnyi (born July 23, 1957, Budapest) is a Hungarian mathematician, doing research in discrete mathematics, particularly finite geometry and algebraic coding theory.
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Tanner graph
In coding theory, a Tanner graph, named after Michael Tanner, is a bipartite graph used to state constraints or equations which specify error correcting codes.
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Ternary Golay code
In coding theory, the ternary Golay codes are two closely related error-correcting codes.
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Theoretical computer science
Theoretical computer science, or TCS, is a subset of general computer science and mathematics that focuses on more mathematical topics of computing and includes the theory of computation.
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Theory
A theory is a contemplative and rational type of abstract or generalizing thinking, or the results of such thinking.
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Thomas Zaslavsky
Thomas Zaslavsky (born 1945) is an American mathematician specializing in combinatorics.
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Triangular network coding
In coding theory, triangular network coding (TNC) is a network coding based packet coding scheme introduced by.
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Underdetermined system
In mathematics, a system of linear equations or a system of polynomial equations is considered underdetermined if there are fewer equations than unknowns (in contrast to an overdetermined system, where there are more equations than unknowns).
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Variable-length code
In coding theory a variable-length code is a code which maps source symbols to a variable number of bits.
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Vámos matroid
In mathematics, the Vámos matroid or Vámos cube is a matroid over a set of eight elements that cannot be represented as a matrix over any field.
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Vector fields on spheres
In mathematics, the discussion of vector fields on spheres was a classical problem of differential topology, beginning with the hairy ball theorem, and early work on the classification of division algebras.
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Vera Pless
Vera Pless (née Stepen, born March 5, 1931) is an American mathematician specializing in combinatorics and coding theory.
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Volume of an n-ball
In geometry, a ball is a region in space comprising all points within a fixed distance from a given point; that is, it is the region enclosed by a sphere or hypersphere.
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Weissman score
The Weissman score is an efficiency metric for lossless compression applications, which was developed for fictional use.
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Welch bounds
In mathematics, Welch bounds are a family of inequalities pertinent to the problem of evenly spreading a set of unit vectors in a vector space.
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Winnie Li
Wen-Ch'ing (Winnie) Li (born December 25, 1948) is a Taiwanese-American mathematician, a Distinguished Professor of Mathematics at Pennsylvania State University.
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Wozencraft ensemble
In coding theory, the Wozencraft ensemble is a set of linear codes in which most of codes satisfy the Gilbert-Varshamov bound.
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Z-channel (information theory)
A Z-channel is a communications channel used in coding theory and information theory to model the behaviour of some data storage systems.
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Zemor's decoding algorithm
In coding theory, Zemor's algorithm, designed and developed by Gilles Zemor, is a recursive low-complexity approach to code construction.
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Zigzag code
In coding theory, a zigzag code is a type of linear error-correcting code introduced by.
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Redirects here:
Algebraic Coding Theory, Algebraic coding theory, Analog coding, Analog encryption, Channel code, Code theory, Coding Theory, Frequency coding theory.
References
[1] https://en.wikipedia.org/wiki/Coding_theory
