论布尔四元数的正态性

Valérie Gillot, Philippe Langevin, Alexandr Polujan
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引用次数: 0

摘要

在 BFA 2023 会议论文中,A. Polujan、L. Mariot 和 S. Picekex 展示了第一个在维数为 8 的非正态但弱正态弯曲函数的例子。在本论文中,我们提出了基于布尔空间分类的数值方法,以详细探讨 8 变量弯曲函数的正态性,并完善了 S. Dubuc 在维数小于或等于 7 时的结果。基于我们的研究,我们证明了所有 8 变量弯曲函数都是正态或弱正态的。最后,我们猜想,更广义地说,8 变量中所有阶数最多为 4 的布尔函数都是正态函数或弱正态函数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On the normality of Boolean quadrics
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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