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

Properties of a construction f 0 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 (x₁,..., x_2k) ф x_2k+1x_2k+2 (in context of the considered construction) is strengthened.

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