长度为38的极值和$s$ -极值二元自对偶码的分类
Classification of extremal and $s$-extremal binary self-dual codes of length 38
摘要：
本文对长度为38的极值二元自对偶码和$s$ -极值二元自对偶码进行了分类。恰好有2744个极值$[38,19,8]$自对偶码、两个$s$ -极值$[38,19,6]$码和1730个$s$ -极值$[38,19,8]$码。我们得到我们的结果从使用的递归算法中使用的所有极值自对偶代码的长度为36最近的分类，并从一个概括的这种递归算法的阴影。$s$ -极值$[38,19,6]$码的分类允许实现d=6的所有$s$ -极值码的分类。
英文摘要：
In this paper we classify all extremal and $s$-extremal binary self-dual codes of length 38. There are exactly 2744 extremal $[38,19,8]$ self-dual codes, two $s$-extremal $[38,19,6]$ codes, and 1730 $s$-extremal $[38,19,8]$ codes. We obtain our results from the use of a recursive algorithm used in the recent classification of all extremal self-dual codes of length 36, and from a generalization of this recursive algorithm for the shadow. The classification of $s$-extremal $[38,19,6]$ codes permits to achieve the classification of all $s$-extremal codes with d=6.
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