On some properties of self-dual bent functions

We study the properties of self-dual bent functions. It is proved that the minimal Hamming distance between self-dual bent functions is $2^{n/2}$ and the set of self-dual bent functions is a metrically regular set. The necessary and sufficient conditions for the iterative bent functions $\mathcal{BI}$ (A. Canteaut, P. Charpin, 2003) to be self-dual bent have been found. We have proved that there exists a self-dual bent function in $n$ variables and of any degree $d\in\{2,3,\dots,n/2\}$.