Determination for minimum symbol-pair and RT weights via torsional degrees of repeated-root cyclic codes

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

Applicable Algebra in Engineering Communication and Computing Pub Date : 2023-04-26 DOI:10.1007/s00200-023-00605-7

Boran Kim

引用次数: 0

Abstract

There are various metrics for researching error-correcting codes. Especially, high-density data storage system gives the existence of inconsistency for the reading and writing process. The symbol-pair metric is motivated for outputs that have overlapping pairs of symbols in a certain channel. The Rosenbloom–Tsfasman (RT) metric is introduced since there exists a problem that is related to transmission over several parallel communication channels with some channels not available for the transmission. In this paper, we determine the minimum symbol-pair weight and RT weight of repeated-root cyclic codes over \(\mathfrak R=\mathbb {F}_{p^m}[u]/\langle u^4\rangle \) of length \(n=p^k\). For the determination, we explicitly present third torsional degree for all different types of cyclic codes over \(\mathfrak R\) of length n.

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通过重根循环码的扭转度确定最小符号对和RT权值

纠错码的研究有多种指标。特别是在高密度数据存储系统中，读写过程存在不一致性。符号对度量是针对某一信道中存在重叠符号对的输出而提出的。引入 Rosenbloom-Tsfasman (RT) 度量是因为存在一个问题，即在多个并行通信信道上进行传输时，某些信道无法用于传输。本文确定了长度为 \(n=p^k\) 的 \(\mathfrak R=\mathbb {F}_{p^m}[u]/\langle u^4\rangle \) 上重复根循环码的最小符号对权重和 RT 权重。为了确定这一点，我们明确提出了长度为 n 的 \(\mathfrak R\) 上所有不同类型循环码的第三扭转度。

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.