English

New Set of Codes for the Maximum-Likelihood Decoding Problem

Information Theory 2010-11-17 v1 math.IT

Abstract

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 codes, including two codes for which the maximum-likelihood decoding problem can be solved in quasi-quadratic time.

Keywords

Cite

@article{arxiv.1011.2834,
  title  = {New Set of Codes for the Maximum-Likelihood Decoding Problem},
  author = {Morgan Barbier},
  journal= {arXiv preprint arXiv:1011.2834},
  year   = {2010}
}

Comments

in Yet Another Conference on Cryptography, Porquerolle : France (2010)

R2 v1 2026-06-21T16:42:44.772Z