Properties of bent functions with minimal distance

The minimal Hamming distance $2^{n/2}$ between distinct bent functions of $n$ variables is obtained. We prove that two bent functions are at the minimal distance if and only if the set of vectors for which they differ is a linear manifold and both functions are affine ones on it. We give an algorithm for constructing all the bent functions being at the minimal distance from the given bent function. Some experimental data are presented for bent functions of the small number of variables.