关于Kerdock码的分支和BCH码的对偶$C_{1,3}$
On components of a Kerdock code and the dual of the BCH code $C_{1,3}$
摘要：
本文研究了两类码的$i$ -分量的结构：Kerdock码和长度为$n=2^m-1$的设计距离为5的本原循环BCH码的$i$-分量的结构，其中对奇数的$m$ .证明了对任意容许长度，删余Kerdock码都由两个$i$ -分量组成，并且对任意$i$，BCH码的对偶都是一个$i$ -分量.我们给出了另一种证明的事实，由德卡昂和范达姆在1999年提出的限制的汉明计划的双缩短Kerdock码是一个结合计划。
英文摘要：
In the paper we investigate the structure of $i$-components of two classes of codes: Kerdock codes and the duals of the primitive cyclic BCH code with designed distance 5 of length $n=2^m-1$, for odd $m$. We prove that for any admissible length a punctured Kerdock code consists of two $i$-components and the dual of BCH code is a $i$-component for any $i$. We give an alternative proof for the fact presented by De Caen and van Dam in 1999 that the restriction of the Hamming scheme to a doubly shortened Kerdock code is an association scheme.
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。
