Bent functions in C and D outside the completed Maiorana-McFarland class

Two new classes of bent functions derived from the Maiorana-McFarland class, so-called C and D, were introduced by Carlet two decades ago. However, apart from the subclassD_0, some explicit construction methods for these functions were not provided. Assuming the possibility of specifying a bent function f that belongs to one of these two classes (apart from D_0), the most important issue is then to determine whether f is still contained in the known primary classes or lies outside their completed versions. In this article we partially solve this question by providing sufficient conditions on the permutation and related characteristic function so that f is provably outside the completed Maiorana-McFarland class.