Heuristic decoding of linear codes using commutative algebra

Publikationstyp
Journal Article
Date Issued
2015-07-01
Sprache
English
Author(s)
Schmidt, Natalia  
Zimmermann, Karl-Heinz  
Institut
Eingebettete Systeme E-13  
TORE-URI
http://hdl.handle.net/11420/9814
Journal
Designs, codes and cryptography  
Volume
76
Issue
1
Start Page
23
End Page
35
Citation
Designs, Codes, and Cryptography 76 (1): 23-35 (2015-07-01)
Publisher DOI
10.1007/s10623-014-0008-8
Scopus ID
2-s2.0-85028219144
Each binary linear code can be associated to a binomial ideal which allows for a complete decoding. Two generalizations of the non-binary case given by the ordinary and generalized code ideals have been given which coincide in the binary case and are related by elimination. The approach based on the generalized code ideal provides complete decoding but can be rather cumbersome. In this paper, a new heuristic decoding method based on the ordinary code ideal will be given which can be much faster.
Subjects
Binomial ideal
Gröbner basis
Heuristic decoding
Linear code