From the Euclidean Algorithm for Solving a Key Equation for Dual Reed---Solomon Codes to the Berlekamp---Massey Algorithm

Authors:
Maria Bras-Amorós;Michael E. O'Sullivan
Affiliations:
Departament d'Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili,;Department of Mathematics and Statistics, San Diego State University,
Venue:
AAECC-18 '09 Proceedings of the 18th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Year:
2009

Citing 3
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Abstract

The two primary decoding algorithms for Reed-Solomon codes are the Berlekamp-Massey algorithm and the Sugiyama et al. adaptation of the Euclidean algorithm, both designed to solve a key equation. This article presents a new version of the key equation and a way to use the Euclidean algorithm to solve it. A straightforward reorganization of the algorithm yields the Berlekamp-Massey algorithm.