Weight distribution of codes on hypergraphs
Barg, A.
Mazumdar, A.
Zemor, G.
Dept. of ECE/ISR, Univ. of Maryland, College Park, MD;
This paper appears in: Communication, Control, and Computing, 2008 46th Annual Allerton Conference on
Publication Date: 23-26 Sept. 2008
On page(s): 400-401
Location: Urbana-Champaign, IL,
ISBN: 978-1-4244-2925-7
INSPEC Accession Number: 10501085
Digital Object Identifier: 10.1109/ALLERTON.2008.4797585
Current Version Published: 2009-03-04
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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