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

Article

DOI: 10.1007/s00200-006-0015-8

Cite this article as:
Bras-Amorós, M. & O’Sullivan, M.E. AAECC (2006) 17: 315. doi:10.1007/s00200-006-0015-8

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 (dmin −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.

Keywords

Algebraic geometry codes Orderdomains Decoding Arf semigroups 

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Departament d’Enginyeria de la Informació i de les ComunicacionsUniversitat Autònoma de BarcelonaBellaterraSpain
  2. 2.Department of Mathematics and StatisticsSan Diego State UniversitySan DiegoUSA