Bent Functions

Chapter 13

Bounds on the Number of Bent Functions

Abstract

One of the most important questions in the theory of bent functions is how many there are. If n is equal to 2, 4, 6, or 8, the number of bent functions in n variables is 8, 896, about 2^32.3, and about 2^106.29, respectively. If n > 10, the exact number of bent functions in n variables is still unknown. Moreover, there is a large gap between the lower ($2^{2^{(n/2)+{log}_2(n-2)-1}}$) and upper ($2^{2^{n-1}+\frac{1}{2}\left(\genfrac{}{}{0.0pt}{}{n}{n/2}\right)}$) bounds for this number. There have been several improvements of these bounds, but they are ...