On the normality of Boolean quartics

2024/07/19 by Valérie Gillot, Gillot, Valérie, Philippe Langevin +3 · 1 citation
Computer Science · #06E30 #Advanced Algebra and Logic #Computability, Logic, AI Algorithms #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences

paper · pdf · doi:10.48550/arxiv.2407.14038

openalex publication_date 2024/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the BFA 2023 conference paper, A. Polujan, L. Mariot and S. Picek exhibited the first example of a non-normal but weakly normal bent function in dimension 8. In this note, we present numerical approaches based on the classification of Boolean spaces to explore in detail the normality of bent functions of 8 variables and we complete S. Dubuc s results for dimensions less or equal to 7. Based on our investigations, we show that all bent functions in 8 variables are normal or weakly normal. Finally, we conjecture that more generally all Boolean functions of degree at most 4 in 8 variables are normal or weakly normal.

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