Nonexistence of some ternary linear codes
Nonexistence of some ternary linear codes
复制标题
某些三进制线性码不存在
DOI：
10.1016/j.disc.2021.112572
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发表时间：
2021
影响因子：
0.8
通讯作者：
Maruta Tatsuya
中科院分区：
文献类型：
--
作者：
Sawashima Toshiharu;Maruta Tatsuya
证明了若干维数为6的三元线性码的不存在性，这意味着对于d= 48, 49, 66, 67, 149, 150, n3 (6, d)= g3 (6, d)+ 2，其中g3 (k, d)=∑i= 0 k−1∑d/ 3i²，nq （k, d）表示存在一个[n， k， d] q码的最小长度n。为了通过射影几何证明假设码的不存在性，我们引入了i-Max和i-Max- ns等证明技术来排除码字的一些可能权重。
We prove the nonexistence of some ternary linear codes of dimension 6, which implies that n 3 (6, d)= g 3 (6, d)+ 2 for d= 48, 49, 66, 67, 149, 150, where g 3 (k, d)=∑ i= 0 k− 1⌈ d/3 i⌉ and n q (k, d) denotes the minimum length n for which an [n, k, d] q code exists. To prove the nonexistence of a putative code through projective geometry, we introduce some proof techniques such as i-Max and i-Max-NS to rule out some possible weights of codewords.