{"title":"Array-designed reversible and complementary codes over GF(4)","authors":"Manabu Hagiwara, Whan-Hyuk Choi, Jon-Lark Kim","doi":"10.1007/s00200-023-00622-6","DOIUrl":null,"url":null,"abstract":"<div><p>Array-designed codes are capable of correcting row and column deletions. In this paper, we introduce array-designed reversible and complementary codes over the finite field <i>GF</i>(4), which can correct row deletions and column deletions errors. Hence our codes can be useful for DNA codes. We also propose a construction method of array-designed reversible and complementary codes. As examples, we describe the tensor product of cyclic LCD codes and the tensor product of self-dual reversible codes over <i>GF</i>(4).</p></div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"36 3","pages":"503 - 519"},"PeriodicalIF":0.6000,"publicationDate":"2023-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applicable Algebra in Engineering Communication and Computing","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s00200-023-00622-6","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
Array-designed codes are capable of correcting row and column deletions. In this paper, we introduce array-designed reversible and complementary codes over the finite field GF(4), which can correct row deletions and column deletions errors. Hence our codes can be useful for DNA codes. We also propose a construction method of array-designed reversible and complementary codes. As examples, we describe the tensor product of cyclic LCD codes and the tensor product of self-dual reversible codes over GF(4).
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.
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