A bent function construction by a bent function that is affine on several cosets of a linear subspace

A construction of bent functions by a given bent function is introduced. Let f be a bent function in 2k variables and, for some w E F^^fc, the bent function f (x) ф (w,x) is constant on each of distinct cosets C₁,..., C₂2k-2t of some t-dimensional linear subspace of F|^fc, where 0 ^ t ^ k. Then f ф Indc₁u...uc₂2fc-2t is a bent function too. This is a generalization of the construction of bent functions at the minimal possible Hamming distance from a given bent function. For t = 2 and for a quadratic bent function f, a simplification of the construction is done. It is proved that the construction generates not more than t-1 2* П (2^2k-2i - 1)/(2^t-i - 1) bent functions for an arbitrary bent function f and a fixed t. i=0 For t ^ 2, the bound is attainable if and only if f is quadratic.

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