{"title":"超图上码的权值分布","authors":"A. Barg, A. Mazumdar, G. Zémor","doi":"10.1109/ALLERTON.2008.4797585","DOIUrl":null,"url":null,"abstract":"Codes on hypergraphs are an extension of the well-studied family of codes on bipartite graphs. Bilu and Hoory (2004) constructed an explicit family of codes on regular t-partite hypergraphs whose minimum distance improves earlier estimates of the distance of bipartite-graph codes. In this talk we compute asymptotic weight distribution of several ensembles of hypergraph codes, establishing conditions under which they attain the Gilbert-Varshamov bound and deriving estimates of their distance. In particular, we show that this bound is attained by codes constructed on a fixed bipartite graph with a large spectral gap.","PeriodicalId":120561,"journal":{"name":"2008 46th Annual Allerton Conference on Communication, Control, and Computing","volume":"10 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2008-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Weight distribution of codes on hypergraphs\",\"authors\":\"A. Barg, A. Mazumdar, G. Zémor\",\"doi\":\"10.1109/ALLERTON.2008.4797585\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Codes on hypergraphs are an extension of the well-studied family of codes on bipartite graphs. Bilu and Hoory (2004) constructed an explicit family of codes on regular t-partite hypergraphs whose minimum distance improves earlier estimates of the distance of bipartite-graph codes. In this talk we compute asymptotic weight distribution of several ensembles of hypergraph codes, establishing conditions under which they attain the Gilbert-Varshamov bound and deriving estimates of their distance. In particular, we show that this bound is attained by codes constructed on a fixed bipartite graph with a large spectral gap.\",\"PeriodicalId\":120561,\"journal\":{\"name\":\"2008 46th Annual Allerton Conference on Communication, Control, and Computing\",\"volume\":\"10 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2008-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2008 46th Annual Allerton Conference on Communication, Control, and Computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ALLERTON.2008.4797585\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2008 46th Annual Allerton Conference on Communication, Control, and Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ALLERTON.2008.4797585","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Codes on hypergraphs are an extension of the well-studied family of codes on bipartite graphs. Bilu and Hoory (2004) constructed an explicit family of codes on regular t-partite hypergraphs whose minimum distance improves earlier estimates of the distance of bipartite-graph codes. In this talk we compute asymptotic weight distribution of several ensembles of hypergraph codes, establishing conditions under which they attain the Gilbert-Varshamov bound and deriving estimates of their distance. In particular, we show that this bound is attained by codes constructed on a fixed bipartite graph with a large spectral gap.
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