{"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}
引用次数: 0
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.
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