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Weight distribution and decoding of codes on hypergraphs

hal.structure.identifierDept. of ECE and Institute for Systems Research, university of Maryland
dc.contributor.authorBARG, Alexander
hal.structure.identifierDept. of ECE and Institute for Systems Research, university of Maryland
dc.contributor.authorMAZUMDAR, Arya
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorZÉMOR, Gilles
dc.date.accessioned2024-04-04T02:43:34Z
dc.date.available2024-04-04T02:43:34Z
dc.date.created2008-11
dc.date.issued2008-11
dc.identifier.issn1930-5346
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191343
dc.description.abstractEnCodes 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. They also suggested a decoding algorithm for such codes and estimated its error-correcting capability. In this paper we study two aspects of hypergraph codes. First, we compute the weight enumerators of several ensembles of such 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. We also suggest a new decoding algorithm of hypergraph codes that corrects a constant fraction of errors, improving upon the algorithm of Bilu and Hoory.
dc.language.isoen
dc.publisherAIMS
dc.title.enWeight distribution and decoding of codes on hypergraphs
dc.typeArticle de revue
dc.identifier.doi10.3934/amc.2008.2.433
dc.subject.halInformatique [cs]/Théorie de l'information [cs.IT]
dc.identifier.arxiv0808.3453
bordeaux.journalAdvances in Mathematics of Communications
bordeaux.page433 - 450
bordeaux.volume2
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue4
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00346971
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00346971v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Advances%20in%20Mathematics%20of%20Communications&rft.date=2008-11&rft.volume=2&rft.issue=4&rft.spage=433%20-%20450&rft.epage=433%20-%20450&rft.eissn=1930-5346&rft.issn=1930-5346&rft.au=BARG,%20Alexander&MAZUMDAR,%20Arya&Z%C3%89MOR,%20Gilles&rft.genre=article


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