论文标题
twe_generalizations_for_quadratic_residue_codes_over_finite_fields
Two_Generalizations_for_Quadratic_Residue_Codes_over_Finite_Fields
论文作者
论文摘要
众所周知，有限场上的二次残基代码是一类有趣的循环代码，适用于其最小距离。令$ g $为正整数，$ p，p_ {1}，\ ldots，p_ {g} $是独特的奇数，本文概括了具有长度$ p $的二次残留代码的构造，以$ n = p _ = p_ {1}} \ cd p _ cdots p_ p_ {g} $ pue cas $ - $ M \ GEQ 2 $是一个正整数。此外，获得这些代码是自动式或互补双重的标准，然后给出相应的计数公式。特别是，确定了所有24个二次二次残留码的最小距离$ [15,8] $。
It's well known that the quadratic residue code over finite fields is an interesting class of cyclic codes for its higher minimum distance. Let $g$ be a positive integer and $p,p_{1},\ldots, p_{g}$ be distinct odd primes, the present paper generalizes the constructions for the quadratic residue code with length $p$ to be the length $n=p_{1}\cdots p_{g}$, and to be the case $m$-th residue codes with length $p$ over finite fields, where $m\geq 2$ is a positive integer. Furthermore, a criterion for that these codes are self-orthogonal or complementary dual is obtained, and then the corresponding counting formula are given. In particular, the minimum distance of all 24 quaternary quadratic residue codes $[15,8]$ are determined.
