On the set of values for Hamming distance between self-dual bent functions

It is shown that the Hamming distance between self-dual Maiorana–McFarland bent functions of the form $\langle x,\pi(y)\rangle\oplus h(y)$, where $\pi\in\operatorname{GL}(n/2,\mathbb Z_2)$, belongs to the set $\{2^{n-1},2^{n-1}(1\pm1/2),2^{n-1}(1\pm1/2^2),\dots,2^{n-1}(1\pm1/2^{n/2-1}),2^n\}$.