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Chelyabinskiy Fiziko-Matematicheskiy Zhurnal, 2020, Volume 5, Issue 3, Pages 327–341
DOI: https://doi.org/10.47475/2500-0101-2020-15307 (Mi chfmj192) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Mathematics

On decoding algorithms for Goppa codes

S. M. Ratseev

Ulyanovsk State University, Ulyanovsk, Russia
Full-text PDF (736 kB) Citations (6)
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DOI: https://doi.org/10.47475/2500-0101-2020-15307
Abstract: The paper is devoted to the decoding algorithms for Goppa codes. These codes are an important part of some promising post-quantum cryptographic algorithms. The Patterson algorithm is well known for decoding Goppa codes, but it is only applicable for binary codes. Since Goppa codes can be specified using generalized Reed — Solomon codes, any decoding algorithm for such codes is also applicable to Goppa codes. The algorithms for decoding Goppa codes based on the algorithm Sugiyama algorithm, Gao algorithm, Berlekamp — Massey algorithm (Peterson — Gorenstein — Zierler algorithm) are given. The Patterson algorithm is also given.
Keywords: error-correcting code, Goppa code, Reed — Solomon code, code decoding.
Received: 21.04.2020
Revised: 15.07.2020
Document Type: Article
UDC: 519.725
Language: Russian
Citation: S. M. Ratseev, “On decoding algorithms for Goppa codes”, Chelyab. Fiz.-Mat. Zh., 5:3 (2020), 327–341
Citation in format AMSBIB
\Bibitem{Rat20}
\by S.~M.~Ratseev
\paper On decoding algorithms for Goppa codes
\jour Chelyab. Fiz.-Mat. Zh.
\yr 2020
\vol 5
\issue 3
\pages 327--341
\mathnet{http://mi.mathnet.ru/chfmj192}
\crossref{https://doi.org/10.47475/2500-0101-2020-15307}
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  • https://www.mathnet.ru/eng/chfmj/v5/i3/p327
    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Chelyabinskiy Fiziko-Matematicheskiy Zhurnal
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