New Set of Codes for the Maximum-Likelihood Decoding Problem [article]

Morgan Barbier
2010 arXiv   pre-print
The maximum-likelihood decoding problem is known to be NP-hard for general linear and Reed-Solomon codes. 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 bi- nary BCH codes, we were able to find several examples of A-covered
more » ... odes, including two codes for which the maximum-likelihood decoding problem can be solved in quasi-quadratic time.
arXiv:1011.2834v1 fatcat:opy5a4ipsbagrgdwbiluidfdkm