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Vestnik Samarskogo Universiteta. Estestvenno-Nauchnaya Seriya, 2021, Volume 27, Issue 1, Pages 44–61
DOI: https://doi.org/10.18287/2541-7525-2021-27-1-44-61
(Mi vsgu646)
 

This article is cited in 3 scientific papers (total in 3 papers)

Mathematics

On the Berlekamp — Massey algorithm and its application for decoding algorithms

S. M. Ratseev, A. D. Lavrinenko, E. A. Stepanova

Ulyanovsk State University, Ulyanovsk, Russian Federation (published under the terms of the Creative Commons Attribution 4.0 International License)
References:
Abstract: The paper is devoted to the Berlekamp — Masssey algorithm and its equivalent version based on the extended Euclidean algorithm. An optimized Berlekamp — Massey algorithm is also given for the case of a field of characteristic 2. The Berlekamp — Massey algorithm has a quadratic complexity and is used, for example, to solve systems of linear equations in which the matrix of the system is the Toeplitz matrix. In particular, such systems of equations appear in algorithms for the syndrome decoding of BCH codes, Reed — Solomon codes, generalized Reed — Solomon codes, and Goppa codes. Algorithms for decoding the listed codes based on the Berlekamp — Massey algorithm are given.
Keywords: Berlekamp — Massey algorithm, extended Euclidean algorithm, Reed — Solomon codes, code decoding.
Received: 10.01.2021
Revised: 17.02.2021
Accepted: 28.02.2021
Document Type: Article
UDC: 512.531; 519.7
Language: Russian
Citation: S. M. Ratseev, A. D. Lavrinenko, E. A. Stepanova, “On the Berlekamp — Massey algorithm and its application for decoding algorithms”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 27:1 (2021), 44–61
Citation in format AMSBIB
\Bibitem{RatLavSte21}
\by S.~M.~Ratseev, A.~D.~Lavrinenko, E.~A.~Stepanova
\paper On the Berlekamp~--- Massey algorithm and its application for decoding algorithms
\jour Vestnik SamU. Estestvenno-Nauchnaya Ser.
\yr 2021
\vol 27
\issue 1
\pages 44--61
\mathnet{http://mi.mathnet.ru/vsgu646}
\crossref{https://doi.org/10.18287/2541-7525-2021-27-1-44-61}
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  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Вестник Самарского государственного университета. Естественнонаучная серия
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