The Correction Capability of the Berlekamp–Massey–Sakata Algorithm with Majority Voting

Authors:
Maria Bras-Amorós;Michael E. O’Sullivan
Affiliations:
Departament d’Enginyeria de la Informació i de les Comunicacions, Universitat Autònoma de Barcelona, 08193, Bellaterra, Spain;Department of Mathematics and Statistics, San Diego State University, 92182-7720, San Diego, CA, USA
Venue:
Applicable Algebra in Engineering, Communication and Computing
Year:
2006

Citing 0
Cited 4

Algebraic-geometry codes, one-point codes, and evaluation codes

Designs, Codes and Cryptography
Redundancies of correction capability optimized Reed-Muller codes

Discrete Applied Mathematics
On numerical semigroups and the redundancy of improved codes correcting generic errors

Designs, Codes and Cryptography
Extended norm-trace codes with optimized correction capability

AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes

Quantified Score

Hi-index	0.00

Visualization

Abstract

Sakata’s generalization of the Berlekamp–Massey algorithm applies to a broad class of codes defined by an evaluation map on an order domain. In order to decode up to the minimum distance bound, Sakata’s algorithm must be combined with the majority voting algorithm of Feng, Rao and Duursma. This combined algorithm can often decode far more than (d min −1)/2 errors, provided the errors are in general position. We give a precise characterization of the error correction capability of the combined algorithm. We also extend the concept behind Feng and Rao’s improved codes to decoding of errors in general position. The analysis leads to a new characterization of Arf numerical semigroups.