Weight distribution of codes on hypergraphs

Alexander Barg, Arya Mazumdar, Gilles Zémor

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 bipartitegraph 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.

Original languageEnglish (US)
Title of host publication46th Annual Allerton Conference on Communication, Control, and Computing
Pages400-401
Number of pages2
DOIs
StatePublished - Dec 1 2008
Event46th Annual Allerton Conference on Communication, Control, and Computing - Monticello, IL, United States
Duration: Sep 24 2008Sep 26 2008

Publication series

Name46th Annual Allerton Conference on Communication, Control, and Computing

Other

Other46th Annual Allerton Conference on Communication, Control, and Computing
CountryUnited States
CityMonticello, IL
Period9/24/089/26/08

Cite this

Barg, A., Mazumdar, A., & Zémor, G. (2008). Weight distribution of codes on hypergraphs. In 46th Annual Allerton Conference on Communication, Control, and Computing (pp. 400-401). [4797585] (46th Annual Allerton Conference on Communication, Control, and Computing). https://doi.org/10.1109/ALLERTON.2008.4797585