On the normality of Boolean quartics
Discrete Mathematics
2024-07-23 v2
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.
Keywords
Cite
@article{arxiv.2407.14038,
title = {On the normality of Boolean quartics},
author = {Valérie Gillot and Philippe Langevin and Alexandr Polujan},
journal= {arXiv preprint arXiv:2407.14038},
year = {2024}
}