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Applicable Algebra in Engineering, Communication and Computing 2006, Vol. 17 (5 ) :315 -335 doi:10.1007/s00200-006-0015-8 <<-上一篇 下一篇 ->>
The Correction Capability of the Berlekamp–Massey–Sakata Algorithm with Majority Voting
Maria Bras-Amorós(1)   Michael E. O’Sullivan(2)   
1.Universitat Autònoma de Barcelona Departament d’Enginyeria de la Informació i de les Comunicacions 08193 Bellaterra Spain 08193 Bellaterra Spain
2.San Diego State University Department of Mathematics and Statistics San Diego CA 92182-7720 USA San Diego CA 92182-7720 USA
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.
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