New Set of Codes for the Maximum-Likelihood Decoding Problem

The maximum-likelihood decoding problem is known to be NP-hard for general linear and Reed-Solomon codes [1, 4]. In this paper, we introduce the notion of A-covered codes, that is, codes that can be decoded through a polynomial time algorithm A whose decoding bound is beyond the covering radius. For these codes, we show that the maximum-likelihood decoding problem is reachable in polynomial time in the code parameters. Focusing on binary BCH codes, we were able to find several examples of A-covered codes, including two codes for which the maximum-likelihood decoding problem can be solved in quasi-quadratic time.

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Morgan Barbier
• Keywords: Binary Bch Codes, CORR 2010, Education, General Linear, Polynomial Time