Title :
Error-correction capability of binary linear codes
Author :
Helleseth, Tor ; Kløve, Torleiv ; Levenshtein, Vladimir I.
Author_Institution :
Dept. of Informatics, Univ. of Bergen, Norway
fDate :
4/1/2005 12:00:00 AM
Abstract :
The monotone structure of correctable and uncorrectable errors given by the complete decoding for a binary linear code is investigated. New bounds on the error-correction capability of linear codes beyond half the minimum distance are presented, both for the best codes and for arbitrary codes under some restrictions on their parameters. It is proved that some known codes of low rate are as good as the best codes in an asymptotic sense.
Keywords :
Reed-Muller codes; binary codes; decoding; error correction codes; linear codes; Reed-Muller codes; binary linear codes; decoding; error-correction capability; monotone structure; test set; trial set; uncorrectable errors; Councils; Error correction; Error correction codes; Hamming weight; Informatics; Linear code; Mathematics; Maximum likelihood decoding; Testing; Vectors; Error-correction capability; Reed–Muller codes; linear codes; minimal words; monotone functions; test set; trial set;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2005.844080
