On Design-Theoretic Aspects of Boolean and Vectorial Bent Function

There are two construction methods of designs from $(n,m)$ -bent functions, known as translation and addition designs. In this article we analyze, which equivalence relation for Boolean bent i.e. notation="LaTeX">$(n,1)$ vectorial functions with notation="LaTeX">$2\le m\le n/2$ , is coarser: extended-affine or isomorphism associated First, observe that similar to the same concepts all even notation="LaTeX">$n$ notation="LaTeX">$m\le . Further, show inequivalent in variables, whose isomorphic, exist notation="LaTeX">$n\ge 6$ This implies, a coarser than equivalence. However, do not phenomenon small number variables. We classify enumerate six variables show, contrast case, one cannot exhibit isomorphic notation="LaTeX">$(6,m)$ notation="LaTeX">$m\in \{ 2,3 \}$