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Journal Articles Cryptography and Communications - Discrete Structures, Boolean Functions and Sequences Year : 2023

Classification of some cosets of the Reed-Muller code

Abstract

This paper presents a descending method to classify Boolean functions in 7 variables under the action of the affine general linear group. The classification determines the number of classes, a set of orbits representatives and a generator set of the stabilizer of each representative. The method consists in the iteration of the classification process of RM(k, m) / RM(r- 1 , m) from that of RM(k, m)/RM(r, m). We namely obtain the classifications of RM(4, 7)/RM(2, 7) and of RM(7, 7)/RM(3, 7), from which we deduce some consequences on the covering radius of RM(3, 7) and the classification of near bent functions.
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hal-04209845 , version 1 (18-09-2023)

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Valérie Gillot, Philippe Langevin. Classification of some cosets of the Reed-Muller code. Cryptography and Communications - Discrete Structures, Boolean Functions and Sequences , 2023, 15 (6), pp.1129-1137. ⟨10.1007/s12095-023-00652-4⟩. ⟨hal-04209845⟩
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