有限链环上渐近良好的广义拟循环码

IF 0.7 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI:10.3934/amc.2023034

Xiangrui Meng, Jian Gao, Fang-Wei Fu

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引用次数: 0

摘要

在有限链环上构造了一类索引为$ \ well $的广义拟循环码。基于概率论证，讨论了这类码的渐近速率和相对距离。结果表明，有限链环上索引为$ \ well $的GQC码是渐近好的。

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Asymptotically good generalized quasi-cyclic codes over finite chain rings

In this paper, we construct a class of generalized quasi-cyclic (GQC) codes with index $ \ell $ over finite chain rings. Based on probabilistic arguments, we discuss asymptotic rates and relative distances of this class of codes. As a result, we show that GQC codes with index $ \ell $ over finite chain rings are asymptotically good.

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来源期刊

Advances in Mathematics of Communications 工程技术-计算机：理论方法

CiteScore

2.20

自引率

22.20%

发文量

审稿时长

>12 weeks

期刊介绍： Advances in Mathematics of Communications (AMC) publishes original research papers of the highest quality in all areas of mathematics and computer science which are relevant to applications in communications technology. For this reason, submissions from many areas of mathematics are invited, provided these show a high level of originality, new techniques, an innovative approach, novel methodologies, or otherwise a high level of depth and sophistication. Any work that does not conform to these standards will be rejected. Areas covered include coding theory, cryptology, combinatorics, finite geometry, algebra and number theory, but are not restricted to these. This journal also aims to cover the algorithmic and computational aspects of these disciplines. Hence, all mathematics and computer science contributions of appropriate depth and relevance to the above mentioned applications in communications technology are welcome. More detailed indication of the journal''s scope is given by the subject interests of the members of the board of editors.

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