Complete classification of Hadamar'd products of codimension 1 subcodes of Reed-Muller codes

Recieved: 07/03/2023

Accepted: 07/20/2023

Published: 01/27/2024

Keywords: Hadamard product, Shur product, Component-wise product, McEliece public-key cryptosystem, Reed–Muller code, subcode, linear code

To cite this article

Chizhov I.V. Complete classification of Hadamar'd products of codimension 1 subcodes of Reed-Muller codes. // Moscow University Journal. Series 15. Computational Mathematics and Cybernetics. 2024. N 1, p.67-80 https://doi.org/1.55959/MSU/0137-0782-15-2024-47-1-67-80.

This work is licensed under a Сreative Commons Atribiution - NonCommercial 4.0 International (CC BY-NC 4.0)

Chizhov I.V. (Lomonosov Moscow State University (MSU))

Abstract

In this paper, we construct a complete classification of linear codes, which are obtained from codimension 1 subcodes of Reed-Muller codes using Hadamard’s product.