几种少权线性码的权值分布

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.2023037

Huan Sun, Qin Yue, Xue Jia

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引用次数: 0

摘要

在数据存储系统、认证码、关联方案等领域中，权重较小的线性码起着重要的作用。本文构造了$ \mathbb F_{q} $上的6类少权线性码，并利用半原元情况下的高斯周期确定了它们的权分布。有一些权重较小的线性码，其对偶几乎是最大距离可分离码(AMDS)和一些最大距离可分离码(MDS)。

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The weight distributions of several classes of few-weight linear codes

In data storage systems, authentication codes, association schemes, and some other fields, linear codes with few weights play an important role. In this paper, we construct six classes of few weights linear codes over $ \mathbb F_{q} $ and use Gauss periods in the semi-primitive case to determine their weight distributions. There are some linear codes with few weights whose duals are almost Maximum Distance Separable (AMDS) codes and some Maximum Distance Separable (MDS) codes.

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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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