有限交换环上恒环 n-D 码的线性互补对

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

Applicable Algebra in Engineering Communication and Computing Pub Date : 2024-01-19 DOI:10.1007/s00200-023-00640-4

Ridhima Thakral, Sucheta Dutt, Ranjeet Sehmi

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引用次数: 0

摘要

本文获得了一个必要条件，它也是一对有限交换环 R 上的常簇二维编码成为编码 LCP 的充分条件。此外，本文还给出了 R 上非琐碎常环二维码 LCP 的特征，并确定了此类码的总数。上述关于constacyclic 2-D码的结果被扩展到了R上的constacyclic 3-D码。所得到的结果很容易扩展到有限交换环上的constacyclic n-D码，即（n\ge 3\）。此外，还得到了一些关于有限链环上的常环二维码的非三维 LCP 存在性的结果。

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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Linear complementary pairs of constacyclic n-D codes over a finite commutative ring

In this paper, a necessary condition which is sufficient as well for a pair of constacyclic 2-D codes over a finite commutative ring R to be an LCP of codes has been obtained. Also, a characterization of non-trivial LCP of constacyclic 2-D codes over R has been given and total number of such codes has been determined. The above results on constacyclic 2-D codes have been extended to constacyclic 3-D codes over R. The obtained results readily extend to constacyclic n-D codes, \(n \ge 3\), over finite commutative rings. Furthermore, some results on existence of non-trivial LCP of constacyclic 2-D codes over a finite chain ring have been obtained in terms of its residue field.

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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.