论四元赫米提液晶编码的最小权重

Cryptography and Communications Pub Date : 2024-08-20 DOI:10.1007/s12095-024-00733-y

Makoto Araya, Masaaki Harada

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摘要

我们研究了四元赫米提液晶编码中的最大最小权值。我们确定了长度为 n、维数为 k 的四元赫米提液晶码中 \(k \le n \le 17\) 的最大最小权值。我们还首次构造了四元赫米提液晶[21, 5, 13]码和四元赫米提液晶[21, 9, 9]码。还给出了\(k \le n \le 30\) 的四元赫米提液晶[n, k]码中最大最小权值的更新表。

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On the minimum weights of quaternary Hermitian LCD codes

We study the largest minimum weights among quaternary Hermitian LCD codes. We determine the largest minimum weights among quaternary Hermitian LCD codes of length n and dimension k for \(k \le n \le 17\). A quaternary Hermitian LCD [21, 5, 13] code and a quaternary Hermitian LCD [21, 9, 9] code are also constructed for the first time. An updated table of the largest minimum weights among quaternary Hermitian LCD [n, k] codes is also given for \(k \le n \le 30\).

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Cryptography and Communications

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