有限域上渐近良好的 LCD 2-类阿贝尔码

Pub Date : 2024-08-29 DOI:10.1016/j.disc.2024.114224

Guanghui Zhang , Liren Lin , Xuemei Liu

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引用次数: 0

摘要

在本文中，我们构建了一类有限域上的线性互补对偶（简称 LCD）2-类阿贝尔码。基于对这类编码数量的统计和对该类编码中相对最小权值较小的编码数量的估计，我们证明了任意有限域上的 LCD 2-quasi-abelian 编码类是渐近良好的。这类码的存在是无条件的，这与特殊有限域上的自偶 2- 类阿贝尔码的情况不同。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Asymptotically good LCD 2-quasi-abelian codes over finite fields

In this paper, we construct a class of linear complementary dual (LCD for short) 2-quasi-abelian codes over a finite field. Based on counting the number of such codes and estimating the number of the codes in this class whose relative minimum weights are small, we prove that the class of LCD 2-quasi-abelian codes over any finite field is asymptotically good. The existence of such codes is unconditional, which is different from the case of self-dual 2-quasi-abelian codes over a special finite field.

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