Bent functions on the minimal distance

In this paper¹ we show that the minimal Hamming distance in class of bent functions in n variables is equal to 2^n/2. We prove that two bent functions are at the minimal distance if and only if they differ on an affine subspace and these functions are affine on it. We describe a simple algorithm for constructing bent functions at the minimal distance from the given one. We give distribution of Hamming distances for bent functions of small dimension.