三类新的最小距离为4的最优五元循环码

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

Applicable Algebra in Engineering Communication and Computing Pub Date : 2023-08-07 DOI:10.1007/s00200-023-00621-7

Yan Liu, Xiwang Cao

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引用次数: 0

摘要

由于循环码在消费电子、数据存储系统和通信系统中的广泛应用，多年来一直是一个重要的研究课题。最近，在文献中提出了几种形式为\(\mathcal {C}_{(0,1,e)}\)和\(\mathcal {C}_{(1,e,s)}\)的最优五元循环码，其中\(s=\frac{5^m-1}{2}\)和\(2 \le e \le 5^{m}-2\)。本文考虑有限域上某些方程的解，给出了三种新的无限族最优五循环码，其形式为\(\mathcal {C}_{(1,e,s)}\)，参数为\([5^{m}-1, 5^{m}-2m-2, 4]\)。具体来说，我们在吴高飞等人提出的一个开放问题上取得了进展。

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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Three new classes of optimal quinary cyclic codes with minimum distance four

Due to their wide applications in consumer electronics, data storage systems and communication systems, cyclic codes have been an important subject of study for many years. Recently, several classes of optimal quinary cyclic codes of the forms \(\mathcal {C}_{(0,1,e)}\) and \(\mathcal {C}_{(1,e,s)}\) are presented in the literature, where \(s=\frac{5^m-1}{2}\) and \(2 \le e \le 5^{m}-2\). In this paper, by considering the solutions of certain equations over finite fields, we give three new classes of infinite families of optimal quinary cyclic codes of the form \(\mathcal {C}_{(1,e,s)}\) with parameters \([5^{m}-1, 5^{m}-2m-2, 4]\). Specifically, we make progress towards an open problem proposed by Gaofei Wu et al. [17].

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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.