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.

翻译：在BFA 2023会议论文中，A. Polujan、L. Mariot与S. Picek首次展示了8维空间中非正规但弱正规的弯曲函数实例。本文基于布尔空间的分类方法，提出数值计算途径以深入探究8变量弯曲函数的正规性，并完善了S. Dubuc在维度小于等于7时的研究结果。通过系统分析，我们证明所有8变量弯曲函数均具有正规性或弱正规性。最后，我们推测更一般地，所有8变量中次数不超过4的布尔函数都是正规或弱正规的。