Combinatorial bounds for list decoding

Abstract--Informally, an error-correcting code has "nice" listdecodability properties if every Hamming ball of "large" radius has a "small" number of codewords in it. Here, we report linear codes with non-trivial list-decodability: i.e., codes of large rate that are nicely list-decodable, and codes of large distance that are not nicely list-decodable. Specifically, on the positive side, we show that there exist codes of rate R and block length n that have at most c codewords in every Hamming ball of radius H-1 (1 - R - 1/c)

• Type: Journal
• Year: 2002
• Where: TIT
• Authors: Venkatesan Guruswami, Johan Håstad, Madhu Sudan, David Zuckerman
• Keywords: Hamming, Large, Linear Codes, TIT 2002