Character sums over a non-chain ring and their applications

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.2020134

Liqin Qian, X. Cao

引用次数: 1

Abstract

Some valuable results over rings have a promising utilization in coding theory and error-correcting code theory. In this paper, we study character sums over a certain non-chain ring and their applications in codebooks. There are two major ingredients in this study. The first ingredient is to investigate Gaussian sums, hyper Eisenstein sums, Jacobi sums over a certain non-chain ring and study the properties of these character sums. For their applications, the second ingredient is to present three classes of asymptotically optimal codebooks with respect to the Welch bound and a family of optimal codebooks with respect to the Levenshtein bound, which are constructed from character sums over a certain non-chain ring.

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非链环上的字符和及其应用

环上的一些有价值的结果在编码理论和纠错码理论中具有很好的应用前景。本文研究了非链环上的特征和及其在码本中的应用。这项研究有两个主要因素。第一部分是研究非链环上的高斯和、超爱森斯坦和、雅可比和，并研究这些特征和的性质。对于它们的应用，第二部分是给出三类关于Welch界的渐近最优码本和一类关于Levenshtein界的最优码本，它们是由非链环上的字符和构造的。

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

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.