  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.
