We study cubic monomial Boolean functions of the form T r n 1 (µx 2 i +2 j +1) where µ ∈ F 2 n. We prove that the functions of this form do not have any affine derivative if n = i + j or n = 2i − j. Lower bounds on the second order nonlinearities of these functions are derived.
In this paper we consider cubic bent functions obtained by Leander and McGuire (J. Comb. Th. Series A, 116 (2009) 960-970) which are concatenations of quadratic Gold functions. A lower bound of second-order nonlinearities of these functions is obtained. This bound is compared with the lower bounds of second-order nonlinear-ities obtained for functions… (More)