On the minimal distance graph connectivity for bent functions

For the set $\mathcal B_{2k}$ of all bent functions in $2k$ variables, the graph $GB_{2k}$ is defined. The vertices in $GB_{2k}$ are all functions in $\mathcal B_{2k}$ and two of them are adjacent if and only if the Hamming distance between them is equal to $2^k$. It is proved that, for $k=1,2,3$, the graph $GB_{2k}$ is connected and, for any $k$, the subgraph of $GB_{2k}$ induced by the subset of all vertices being affine equivalent to Maiorana–McFarland bent functions is also connected.