{"title":"Perfect Codes in the Johnson Schemes","authors":"T. Etzion","doi":"10.1109/ITW.2006.1633779","DOIUrl":null,"url":null,"abstract":"In his pioneering work, from 1973, on algebraic approach to codes in association schemes, Dlesarte has conjectured that there are no nontrivial perfect codes in the Johnson schemes. Many attempts were made during the last 30 years to solve this conjecture. These attempts used Lloyd polynomials, anticodes in the Johnson schemes, designs, and number theory. We will survey all the known results and outline directions for solving the problem.","PeriodicalId":293144,"journal":{"name":"2006 IEEE Information Theory Workshop - ITW '06 Punta del Este","volume":"26 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2006-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2006 IEEE Information Theory Workshop - ITW '06 Punta del Este","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ITW.2006.1633779","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
In his pioneering work, from 1973, on algebraic approach to codes in association schemes, Dlesarte has conjectured that there are no nontrivial perfect codes in the Johnson schemes. Many attempts were made during the last 30 years to solve this conjecture. These attempts used Lloyd polynomials, anticodes in the Johnson schemes, designs, and number theory. We will survey all the known results and outline directions for solving the problem.
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