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Diskretnaya Matematika, 2020, Volume 32, Issue 1, Pages 115–134
DOI: https://doi.org/10.4213/dm1583 (Mi dm1583) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Classification of Hadamard productsof one-codimensional subcodesof Reed–Muller codes

I. V. Chizhova, M. A. Borodinb

a Lomonosov Moscow State University
b Infotecs, Moscow
Full-text PDF (510 kB) Citations (9)
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DOI: https://doi.org/10.4213/dm1583
Abstract: For Reed–Muller codes we consider subcodes of codimension 1. A classification of Hadamard products of such subcodes is obtained. With the use of this classification it has been shown that in most cases the problem of recovery of the secret key of a code-based cryptosystem employing such subcodes is equivalent to the problem of recovery of the secret key of the same cryptosystem based on Reed–Muller codes, which is known to be tractable.
Keywords: McEliece public key cryptosystem, code-based cryptosystems, Reed–Muller codes, cryptanalysis, Hadamard product, square of a code, classification of Hadamard products, subcodes of codimension 1.
Received: 02.07.2019
Revised: 04.12.2019
English version:
Discrete Mathematics and Applications, 2022, Volume 32, Issue 5, Pages 297–311
DOI: https://doi.org/10.1515/dma-2022-0025
Bibliographic databases:
UDC: 519.719.2
Language: Russian
Citation: I. V. Chizhov, M. A. Borodin, “Classification of Hadamard productsof one-codimensional subcodesof Reed–Muller codes”, Diskr. Mat., 32:1 (2020), 115–134; Discrete Math. Appl., 32:5 (2022), 297–311
Citation in format AMSBIB
\Bibitem{ChiBor20}
\by I.~V.~Chizhov, M.~A.~Borodin
\paper Classification of Hadamard productsof one-codimensional subcodesof Reed--Muller codes
\jour Diskr. Mat.
\yr 2020
\vol 32
\issue 1
\pages 115--134
\mathnet{http://mi.mathnet.ru/dm1583}
\crossref{https://doi.org/10.4213/dm1583}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4075906}
\transl
\jour Discrete Math. Appl.
\yr 2022
\vol 32
\issue 5
\pages 297--311
\crossref{https://doi.org/10.1515/dma-2022-0025}
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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