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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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Preprints, Working Papers, ... (Preprint)
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https://hal-univ-tln.archives-ouvertes.fr/hal-03834481
Contributor : Philippe Langevin Connect in order to contact the contributor
Submitted on : Sunday, October 30, 2022 - 7:20:19 AM
Last modification on : Thursday, November 3, 2022 - 3:24:53 AM

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  • HAL Id : hal-03834481, version 1

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Valérie Gillot, Philippe Langevin. CLASSIFICATION OF SOME COSETS OF THE REED-MULLER CODE. 2022. ⟨hal-03834481⟩

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