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词汇 Quadratic residue code
分类 英语词汇 英语翻译词典
释义

Quadratic residue code

英语百科

Quadratic residue code

A quadratic residue code is a type of cyclic code.

There is a quadratic residue code of length p over the finite field GF(l) whenever p and l are primes, p is odd, and l is a quadratic residue modulo p. Its generator polynomial as a cyclic code is given by

where Q is the set of quadratic residues of p in the set \{1,2,\ldots,p-1\} and  \zeta is a primitive pth root of unity in some finite extension field of GF(l). The condition that l is a quadratic residue of p ensures that the coefficients of f lie in GF(l). The dimension of the code is (p+1)/2. Replacing \zeta by another primitive p-th root of unity \zeta^r either results in the same code or an equivalent code, according to whether or not r is a quadratic residue of p.

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