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Classification of Hadamard products of one-codimensional subcodes of Reed–Muller codes

  • Ivan V. Chizhov EMAIL logo and Mikhail A. Borodin
Published/Copyright: October 12, 2022

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.


Note

Originally published in Diskretnaya Matematika (2020) 32,№1, 115–134 (in Russian).


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Received: 2019-07-02
Revised: 2019-12-04
Published Online: 2022-10-12
Published in Print: 2022-10-26

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