Abstract
On the basis of the results by JL. DORNSTETTER [3] showing the equivalence between BERLEKAMP's and EUCLID's algorithm, we present an iterative Euclidean extended algorithm. We show how all polynomials obtained by the classical extended Euclidean algorithm are actually automatically produced by that iterative process.
In sum, an algorithm is given which is as economical as BERLEKAMP's for decoding and which is proved to perform decoding of alternant codes by the simple argument used for the EUCLIDEAN algorithm.
Finally a result of BERLEKAMP's [1] is exploited to reduce by another half the degrees of all polynomials involved in the decoding process in the particular case of binary BCH codes.
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References
E.R. Berlekamp, "Algebraic Coding Theory" Mc Graw-Hill 1968.
N. Bourbaki, "Eléments de Mathématique" Livre II Algèbre-Chapitre 4 Polynômes et fractions rationnelles. Herman 1959.
JL. Dornstetter, "On the Equivalence Between Berlekamp's and Euclid's Algorithms" IEEE Transactions on Information Theory IT 33 no 3 May 1987.
F.J. MacWilliams and N.J.A. Sloane "The Theory of Error-Correcting Codes" Amsterdam North Holland 1977.
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© 1989 Springer-Verlag Berlin Heidelberg
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Camion, P. (1989). An Iterative Euclidean Algorithm. In: Huguet, L., Poli, A. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1987. Lecture Notes in Computer Science, vol 356. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51082-6_72
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DOI: https://doi.org/10.1007/3-540-51082-6_72
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