This article is cited in 11 papers

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

I. V. Chizhov^a, M. A. Borodin<sup>b

a</sup> Lomonosov Moscow State University
^b Infotecs, Moscow

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.

UDC: 519.719.2

Received: 02.07.2019
Revised: 04.12.2019

DOI: 10.4213/dm1583

 English version: Discrete Mathematics and Applications, 2022, 32:5, 297–311

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