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

IF 0.7 3区数学 Q2 MATHEMATICS

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

Guanghui Zhang , Liren Lin , Xuemei Liu

引用次数: 0

Abstract

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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有限域上渐近良好的 LCD 2-类阿贝尔码

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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来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.