{"title":"最大见证码的一些构造","authors":"Nikolaos Makriyannis, Bertrand Meyer","doi":"10.1109/ISIT.2011.6033928","DOIUrl":null,"url":null,"abstract":"Given a code C ∈ F<sup>n</sup><inf>2</inf> and a word c ∈ C, a witness of c is a subset W ⊆ {, 1∦, n} of coordinate positions such that c differs from any other codeword c′ ∈ C on the indices in W. If any codeword posseses a witness of given length w, C is called a w-witness code. This paper gives new constructions of large w-witness codes and proves with a numerical method that their sizes are maximal for certain values of n and w. Our technique is in the spirit of Delsarte's linear programming bound on the size of classical codes and relies on the Lovász theta number, semidefinite programming, and reduction through symmetry.","PeriodicalId":208375,"journal":{"name":"2011 IEEE International Symposium on Information Theory Proceedings","volume":"53 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2011-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Some constructions of maximal witness codes\",\"authors\":\"Nikolaos Makriyannis, Bertrand Meyer\",\"doi\":\"10.1109/ISIT.2011.6033928\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Given a code C ∈ F<sup>n</sup><inf>2</inf> and a word c ∈ C, a witness of c is a subset W ⊆ {, 1∦, n} of coordinate positions such that c differs from any other codeword c′ ∈ C on the indices in W. If any codeword posseses a witness of given length w, C is called a w-witness code. This paper gives new constructions of large w-witness codes and proves with a numerical method that their sizes are maximal for certain values of n and w. Our technique is in the spirit of Delsarte's linear programming bound on the size of classical codes and relies on the Lovász theta number, semidefinite programming, and reduction through symmetry.\",\"PeriodicalId\":208375,\"journal\":{\"name\":\"2011 IEEE International Symposium on Information Theory Proceedings\",\"volume\":\"53 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2011-10-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2011 IEEE International Symposium on Information Theory Proceedings\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISIT.2011.6033928\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2011 IEEE International Symposium on Information Theory Proceedings","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISIT.2011.6033928","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Given a code C ∈ Fn2 and a word c ∈ C, a witness of c is a subset W ⊆ {, 1∦, n} of coordinate positions such that c differs from any other codeword c′ ∈ C on the indices in W. If any codeword posseses a witness of given length w, C is called a w-witness code. This paper gives new constructions of large w-witness codes and proves with a numerical method that their sizes are maximal for certain values of n and w. Our technique is in the spirit of Delsarte's linear programming bound on the size of classical codes and relies on the Lovász theta number, semidefinite programming, and reduction through symmetry.
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