ON DECODING ALGORITHMS FOR GENERALIZED REED — SOLOMON CODES WITH ERRORS AND ERASURES

The article is devoted to the decoding algorithms for generalized Reed Solomon codes with errorsand erasures. These algorithms are based on Gao algorithm, Sugiyama algorithm, Berlekamp Massey algorithm (Peterson Gorenstein Zierler algorithm). The first of these algorithms belongs to syndrome-free de...

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Published inVestnik of Samara University Natural Science Series Vol. 26; no. 3; pp. 17 - 29
Main Authors Ratseev, S. M., Cherevatenko, O. I.
Format Journal Article
LanguageEnglish
Published 06.05.2020
Online AccessGet full text
ISSN2541-7525
2712-8954
2712-8954
DOI10.18287/2541-7525-2020-26-3-17-29

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Abstract The article is devoted to the decoding algorithms for generalized Reed Solomon codes with errorsand erasures. These algorithms are based on Gao algorithm, Sugiyama algorithm, Berlekamp Massey algorithm (Peterson Gorenstein Zierler algorithm). The first of these algorithms belongs to syndrome-free decoding algorithms, the others to syndrome decoding algorithms. The relevance of these algorithms is that they are applicable for decoding Goppa codes, which are the basis of some promising post-quantum cryptosystems. These algorithms are applicable for Goppa codes over an arbitrary field, as opposed to the well-known Patterson decoding algorithm for binary Goppa codes.
AbstractList The article is devoted to the decoding algorithms for generalized Reed Solomon codes with errorsand erasures. These algorithms are based on Gao algorithm, Sugiyama algorithm, Berlekamp Massey algorithm (Peterson Gorenstein Zierler algorithm). The first of these algorithms belongs to syndrome-free decoding algorithms, the others to syndrome decoding algorithms. The relevance of these algorithms is that they are applicable for decoding Goppa codes, which are the basis of some promising post-quantum cryptosystems. These algorithms are applicable for Goppa codes over an arbitrary field, as opposed to the well-known Patterson decoding algorithm for binary Goppa codes.
Author Cherevatenko, O. I.
Ratseev, S. M.
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