Optimal constacyclic codes with minimum distance four

IF 0.6 4区工程技术 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Applicable Algebra in Engineering Communication and Computing Pub Date : 2024-02-27 DOI:10.1007/s00200-024-00648-4

Yajing Zhou, Xiaoshan Kai, Zhonghua Sun

引用次数: 0

Abstract

Let \(n=2(p^m-1)/(p-1)\), where p is an odd prime and \(m>1\) is a positive integer. In this paper, we research optimal p-ary constacyclic codes with two zeros. Two classes of optimal p-ary \([n,n-2m,4]\) constacyclic codes are presented by searching the solutions of certain congruence equations over \(\mathbb {F}_{p^m}\). Four explicit constructions of optimal constacyclic codes with such parameters are provided. The dual codes of a subclass of these constacyclic codes are also investigated.

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距离最小的最优常环码四

让（n=2(p^m-1)/(p-1)\），其中 p 是奇素数，\(m>1\)是正整数。本文研究了具有两个零的最优 pary 常环码。通过搜索 \(\mathbb {F}_{p^m}\) 上某些全等方程的解，提出了两类最优 pary \([n,n-2m,4]\)constacyclic码。本文提供了四种具有此类参数的最优constacyclic编码的明确构造。此外，还研究了这些常环码的一个子类的对偶码。

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

Applicable Algebra in Engineering Communication and Computing 工程技术-计算机：跨学科应用

CiteScore

2.90

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Algebra is a common language for many scientific domains. In developing this language mathematicians prove theorems and design methods which demonstrate the applicability of algebra. Using this language scientists in many fields find algebra indispensable to create methods, techniques and tools to solve their specific problems. Applicable Algebra in Engineering, Communication and Computing will publish mathematically rigorous, original research papers reporting on algebraic methods and techniques relevant to all domains concerned with computers, intelligent systems and communications. Its scope includes, but is not limited to, vision, robotics, system design, fault tolerance and dependability of systems, VLSI technology, signal processing, signal theory, coding, error control techniques, cryptography, protocol specification, networks, software engineering, arithmetics, algorithms, complexity, computer algebra, programming languages, logic and functional programming, algebraic specification, term rewriting systems, theorem proving, graphics, modeling, knowledge engineering, expert systems, and artificial intelligence methodology. Purely theoretical papers will not primarily be sought, but papers dealing with problems in such domains as commutative or non-commutative algebra, group theory, field theory, or real algebraic geometry, which are of interest for applications in the above mentioned fields are relevant for this journal. On the practical side, technology and know-how transfer papers from engineering which either stimulate or illustrate research in applicable algebra are within the scope of the journal.