Reed-Muller码的一维子码的Hadamard产品分类

IF 0.3 Q4 MATHEMATICS, APPLIED

Discrete Mathematics and Applications Pub Date : 2022-10-01 DOI:10.1515/dma-2022-0025

I. Chizhov, M. Borodin

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引用次数: 0

摘要

对于Reed-Muller码，我们考虑余维数为1的子码。得到了这种子码的Hadamard产品的分类。使用这种分类表明，在大多数情况下，使用这种子码的基于代码的密码系统的密钥恢复问题相当于基于里德-穆勒码的相同密码系统的密钥恢复问题，这是已知的可处理的。

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

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.

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来源期刊

Discrete Mathematics and Applications MATHEMATICS, APPLIED-

CiteScore

0.60

自引率

20.00%

发文量

期刊介绍： The aim of this journal is to provide the latest information on the development of discrete mathematics in the former USSR to a world-wide readership. The journal will contain papers from the Russian-language journal Diskretnaya Matematika, the only journal of the Russian Academy of Sciences devoted to this field of mathematics. Discrete Mathematics and Applications will cover various subjects in the fields such as combinatorial analysis, graph theory, functional systems theory, cryptology, coding, probabilistic problems of discrete mathematics, algorithms and their complexity, combinatorial and computational problems of number theory and of algebra.