Double skew cyclic codes over $$\mathbb {F}_q+v\mathbb {F}_q$$

IF 0.6 4区工程技术 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Applicable Algebra in Engineering Communication and Computing Pub Date : 2024-09-15 DOI:10.1007/s00200-024-00668-0

Ashutosh Singh, Tulay Yildirim, Om Prakash

引用次数: 0

Abstract

In order to get a better code rate, this study focuses on the construction of double skew cyclic codes over the ring $\textrm{R}= \mathbb {F}_q+v\mathbb {F}_q$ with $v^2=v$, where q is a prime power. We investigate the generator polynomials, minimal spanning sets, generator matrices, and the dual codes over the ring $\textrm{R}$. As an implementation, the obtained results are illustrated with some suitable examples. Here, we introduce a construction for new generator matrices and thus achieve codes with improved parameters compared to those available in the existing literature. Finally, we tabulate our obtained codes over the ring $\textrm{R}$.

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在 $$\mathbb {F}_q+v\mathbb {F}_q$ 上的双斜循环码

为了获得更好的编码率，本研究重点关注在环$\textrm{R}= \mathbb {F}_q+v\mathbb {F}_q$上构建双斜循环码，其中 q 是素幂。我们研究了环$textrm{R}$上的生成器多项式、最小跨集、生成器矩阵和对偶码。作为实现，我们用一些合适的例子来说明所获得的结果。在这里，我们引入了一种新的生成矩阵结构，从而实现了与现有文献相比参数有所改进的编码。最后，我们列出了我们在环（textrm{R}\）上获得的编码。

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.