{"title":"与三角图和Kn的范畴积有关的图的代码","authors":"K. Kumwenda, E. Mwambene","doi":"10.1109/CIG.2010.5592662","DOIUrl":null,"url":null,"abstract":"For any prime p and n ⋛ 3, we examine p-ary linear codes generated by incidence matrices of two classes of graphs, H<inf>n</inf> and Γ<inf>n</inf> where H<inf>n−1</inf> is an induced subgraph of Γ<inf>n</inf>. Γ<inf>n</inf> is a subgraph of the union of the categorical product of triangular graphs T<inf>n</inf> and complete graphs K<inf>n</inf>, and complements of triangular graphs T<inf>n</inf> and K<inf>n</inf>, where the union of graphs is as defined in [4]. For the codes of H<inf>n</inf>, we exhibit permutation decoding sets of order n for full error correction. Their size is only twice the lower bound due to Gordon [7]. We also consider partial permutation decoding for the binary codes from Γ<inf>n</inf>.","PeriodicalId":354925,"journal":{"name":"2010 IEEE Information Theory Workshop","volume":"57 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2010-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Codes from graphs related to the categorical product of triangular graphs and Kn\",\"authors\":\"K. Kumwenda, E. Mwambene\",\"doi\":\"10.1109/CIG.2010.5592662\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For any prime p and n ⋛ 3, we examine p-ary linear codes generated by incidence matrices of two classes of graphs, H<inf>n</inf> and Γ<inf>n</inf> where H<inf>n−1</inf> is an induced subgraph of Γ<inf>n</inf>. Γ<inf>n</inf> is a subgraph of the union of the categorical product of triangular graphs T<inf>n</inf> and complete graphs K<inf>n</inf>, and complements of triangular graphs T<inf>n</inf> and K<inf>n</inf>, where the union of graphs is as defined in [4]. For the codes of H<inf>n</inf>, we exhibit permutation decoding sets of order n for full error correction. Their size is only twice the lower bound due to Gordon [7]. We also consider partial permutation decoding for the binary codes from Γ<inf>n</inf>.\",\"PeriodicalId\":354925,\"journal\":{\"name\":\"2010 IEEE Information Theory Workshop\",\"volume\":\"57 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2010-09-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2010 IEEE Information Theory Workshop\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/CIG.2010.5592662\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2010 IEEE Information Theory Workshop","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CIG.2010.5592662","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Codes from graphs related to the categorical product of triangular graphs and Kn
For any prime p and n ⋛ 3, we examine p-ary linear codes generated by incidence matrices of two classes of graphs, Hn and Γn where Hn−1 is an induced subgraph of Γn. Γn is a subgraph of the union of the categorical product of triangular graphs Tn and complete graphs Kn, and complements of triangular graphs Tn and Kn, where the union of graphs is as defined in [4]. For the codes of Hn, we exhibit permutation decoding sets of order n for full error correction. Their size is only twice the lower bound due to Gordon [7]. We also consider partial permutation decoding for the binary codes from Γn.
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