{"title":"The error-correcting pair for direct sum codes","authors":"Boyi He, Qunying Liao","doi":"10.3934/amc.2023046","DOIUrl":null,"url":null,"abstract":"The error-correcting pair is a general algebraic decoding method for linear codes, which exists for many classical linear codes. In this paper, we focus our study on the error-correcting pair for the direct sum code of two linear codes with an error-correcting pair. Firstly, for the direct sum code $ \\mathcal{C} $ of two linear codes with an error-correcting pair, several sufficient conditions for $ \\mathcal{C} $ with an error-correcting pair are given. Secondly, for the direct sum code $ \\mathcal{C} $ of two Maximal Distance Separable linear codes, two Near-Maximal Distance Separable linear codes, or a Maximal Distance Separable linear code and a Near-Maximal Distance Separable linear code, several sufficient conditions for $ \\mathcal{C} $ with an error-correcting pair are given, respectively. And then, we introduce the corresponding decoding procedure of the direct sum code with an error-correcting pair, and give several examples.","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":"40 1","pages":"0"},"PeriodicalIF":0.7000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Mathematics of Communications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/amc.2023046","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
The error-correcting pair is a general algebraic decoding method for linear codes, which exists for many classical linear codes. In this paper, we focus our study on the error-correcting pair for the direct sum code of two linear codes with an error-correcting pair. Firstly, for the direct sum code $ \mathcal{C} $ of two linear codes with an error-correcting pair, several sufficient conditions for $ \mathcal{C} $ with an error-correcting pair are given. Secondly, for the direct sum code $ \mathcal{C} $ of two Maximal Distance Separable linear codes, two Near-Maximal Distance Separable linear codes, or a Maximal Distance Separable linear code and a Near-Maximal Distance Separable linear code, several sufficient conditions for $ \mathcal{C} $ with an error-correcting pair are given, respectively. And then, we introduce the corresponding decoding procedure of the direct sum code with an error-correcting pair, and give several examples.
期刊介绍：
Advances in Mathematics of Communications (AMC) publishes original research papers of the highest quality in all areas of mathematics and computer science which are relevant to applications in communications technology. For this reason, submissions from many areas of mathematics are invited, provided these show a high level of originality, new techniques, an innovative approach, novel methodologies, or otherwise a high level of depth and sophistication. Any work that does not conform to these standards will be rejected.
Areas covered include coding theory, cryptology, combinatorics, finite geometry, algebra and number theory, but are not restricted to these. This journal also aims to cover the algorithmic and computational aspects of these disciplines. Hence, all mathematics and computer science contributions of appropriate depth and relevance to the above mentioned applications in communications technology are welcome.
More detailed indication of the journal''s scope is given by the subject interests of the members of the board of editors.
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