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13 relations: Coding theory, Cryptography, Cyclotomic polynomial, Equally spaced polynomial, Finite field, GF(2), Hamming weight, Irreducible polynomial, Multiplication, Polynomial, Primitive polynomial (field theory), Primitive root modulo n, Root of unity.
Coding theory
Coding theory is the study of the properties of codes and their respective fitness for specific applications.
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Cryptography
Cryptography or cryptology (from κρυπτός|translit.
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Cyclotomic polynomial
In mathematics, more specifically in algebra, the nth cyclotomic polynomial, for any positive integer n, is the unique irreducible polynomial with integer coefficients that is a divisor of x^n-1 and is not a divisor of x^k-1 for any.
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Equally spaced polynomial
An equally spaced polynomial (ESP) is a polynomial used in finite fields, specifically GF(2) (binary).
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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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GF(2)
GF(2) (also F2, Z/2Z or Z2) is the '''G'''alois '''f'''ield of two elements.
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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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Irreducible polynomial
In mathematics, an irreducible polynomial is, roughly speaking, a non-constant polynomial that cannot be factored into the product of two non-constant polynomials.
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Multiplication
Multiplication (often denoted by the cross symbol "×", by a point "⋅", by juxtaposition, or, on computers, by an asterisk "∗") is one of the four elementary mathematical operations of arithmetic; with the others being addition, subtraction and division.
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Polynomial
In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
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Primitive polynomial (field theory)
In field theory, a branch of mathematics, a primitive polynomial is the minimal polynomial of a primitive element of the finite extension field GF(pm).
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Primitive root modulo n
In modular arithmetic, a branch of number theory, a number g is a primitive root modulo n if every number a coprime to n is congruent to a power of g modulo n. That is, for every integer a coprime to n, there is an integer k such that gk ≡ a (mod n).
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Root of unity
In mathematics, a root of unity, occasionally called a de Moivre number, is any complex number that gives 1 when raised to some positive integer power.
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