{"title":"论覆盖半径为 2 和对偶的完全正则码的分类","authors":"J. Borges, V. A. Zinoviev, D. V. Zinoviev","doi":"10.1134/s003294602303002x","DOIUrl":null,"url":null,"abstract":"<p>We classify all linear completely regular codes which have covering radius <span>\\(\\rho=2\\)</span> and whose dual are antipodal. For this, we firstly show several properties of such dual codes, which are two-weight codes with weights <span>\\(d\\)</span> and <span>\\(n\\)</span>.</p>","PeriodicalId":54581,"journal":{"name":"Problems of Information Transmission","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Classification of Completely Regular Codes with Covering Radius Two and Antipodal Duals\",\"authors\":\"J. Borges, V. A. Zinoviev, D. V. Zinoviev\",\"doi\":\"10.1134/s003294602303002x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We classify all linear completely regular codes which have covering radius <span>\\\\(\\\\rho=2\\\\)</span> and whose dual are antipodal. For this, we firstly show several properties of such dual codes, which are two-weight codes with weights <span>\\\\(d\\\\)</span> and <span>\\\\(n\\\\)</span>.</p>\",\"PeriodicalId\":54581,\"journal\":{\"name\":\"Problems of Information Transmission\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-03-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Problems of Information Transmission\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://doi.org/10.1134/s003294602303002x\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Problems of Information Transmission","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1134/s003294602303002x","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
On the Classification of Completely Regular Codes with Covering Radius Two and Antipodal Duals
We classify all linear completely regular codes which have covering radius \(\rho=2\) and whose dual are antipodal. For this, we firstly show several properties of such dual codes, which are two-weight codes with weights \(d\) and \(n\).
期刊介绍：
Problems of Information Transmission is of interest to researcher in all fields concerned with the research and development of communication systems. This quarterly journal features coverage of statistical information theory; coding theory and techniques; noisy channels; error detection and correction; signal detection, extraction, and analysis; analysis of communication networks; optimal processing and routing; the theory of random processes; and bionics.
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