arXiv 1406.57972014-06-23cs.ITmath.IT

F_2上一大类最佳等重码的构造

Constructions of A Large Class of Optimum Constant Weight Codes over F_2

Masao Kasahara, Shigeichi Hirasawa

摘要：

基于广义$(u, u+v)$构造方法，提出了一种构造F2环上最优等重码的新方法。提出了一种构造叠加码$C_{(s_1,s_2,\cdots,s_I)}^{(h_1, h_2, \cdots, h_I)}$界的新方法。并提出了F_2上满足Brouwer和Verhoeff界的一类最优等重码BV。本文给出了F_2上$k=2$和$n \leqq 128$上$k=3$的最优等重码的大类.我们还提出了F_2上的最优等重码，它们满足$k=2,3,4,5$的BV界和$n \leqq 128$的BV界。本文提出的$C_{I}$：$C_{(s_1)}^{(h_1)}$给出了码长$n=3h_1$、信息码元数$k=2$和最小距离$d=2h_1$的最佳等重码。$C_{II}$：对于任何$h_1$，$C_{(s_1)}^{(h_1)}$在$n=7h_1, k=3$和$d=4h_1$处产生最佳等重码。$C_{III}$：码$C_{(s_1,s_2,\cdots,s_I)}^{(h_1, h_2, \cdots, h_I)}$产生长度为$n=2^{k+1}-2$的最佳等重码，以及对于任何数目的信息符号$k\geq 3$的最小距离$d=2^{k}$。

英文摘要：

A new method of constructing optimum constant weight codes over F_2 based on a generalized $(u, u+v)$ construction is presented. We present a new method of constructing superimposed code $C_{(s_1,s_2,\cdots,s_I)}^{(h_1, h_2, \cdots, h_I)}$ bound. and presented a large class of optimum constant weight codes over F_2 that meet the bound due to Brouwer and Verhoeff, which will be referred to as BV . We present large classes of optimum constant weight codes over F_2 for $k=2$ and $k=3$ for $n \leqq 128$. We also present optimum constant weight codes over F_2 that meet the BV bound for $k=2,3,4,5$ and 6, for $n \leqq 128$. The authors would like to present the following conjectures : $C_{I}$: $C_{(s_1)}^{(h_1)}$ presented in this paper yields the optimum constant weight codes for the code-length $n=3h_1$, number of information symbols $k=2$ and minimum distance $d=2h_1$ for any positive integer $h_1$. $C_{II}$: $C_{(s_1)}^{(h_1)}$ yields the optimum constant weight codes at $n=7h_1, k=3$ and $d=4h_1$ for any $h_1$. $C_{III}$: Code $C_{(s_1,s_2,\cdots,s_I)}^{(h_1, h_2, \cdots, h_I)}$ yields the optimum constant weight codes of length $n=2^{k+1}-2$, and minimum distance $d=2^{k}$ for any number of information symbols $k\geq 3$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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