Properties of bent functions constructed by a given bent function using subspaces

Properties of a construction $f \oplus \mathrm{Ind}_L$, where $f$ is a bent function in $2k$ variables and $L$ is an affine subspace, generating bent functions under some conditions are considered. It is proven that the numbers of bent functions generated by $(k + 1)$-dimensional subspaces for a given bent function and its dual function are equal. Some experimental results for bent functions in $6$ and $8$ variables reflecting the number of generated bent functions, equality and inequality of this number for a given bent function and its dual function and nonexistence of generated bent functions if subspaces have some fixed dimensions are presented. Theorem (2018) on subspace connections for bent functions $f$ and $f(x_1, \ldots, x_{2k}) \oplus x_{2k + 1}x_{2k + 2}$ (in context of the considered construction) is strengthened.