NONEXISTENCE OF SOME EXTREMAL SELF-DUAL CODES
NONEXISTENCE OF SOME EXTREMAL SELF-DUAL CODES
复制标题
一些极端自对偶码的不存在
DOI：
10.4134/jkms.2006.43.6.1357
复制
发表时间：
2006
影响因子：
4.5
通讯作者：
June
中科院分区：
文献类型：
--
作者：
Sunghyu Han;June
已知如果C是一个(24m + 2l;12m + l;d )自对偶二进制线性码，且0•l < 11，则d•4m+4。我们提出了一个充分条件，证明d = 4m + 4;l = 1;2;3;5的极值自对偶二进制线性码不存在。从充分条件出发，我们计算出对应于某些极值自对偶二进制线性码不存在的m。特别是，我们证明了存在无限多个这样的 m。对于长度为 n = 6m + 1 的 GF(4) 上的加法自对偶码，我们也给出了类似的结果。
It is known that if C is an (24m + 2l;12m + l;d ) self- dual binary linear code with 0 • l < 11, then d • 4m + 4. We present a su-cient condition for the nonexistence of extremal self- dual binary linear codes with d = 4m + 4;l = 1;2;3;5. From the su-cient condition, we calculate m's which correspond to the nonexistence of some extremal self-dual binary linear codes. In particular, we prove that there are inflnitely many such m's. We also give similar results for additive self-dual codes over GF(4) of length n = 6m + 1.