I. Introduction
The properties of quadratic Boolean functions (i.e., the second order Reed–Muller code ) are well studied, (e.g., the weight distribution [1], the affine equivalence classes [1], the classification of resilient functions [2] and functions satisfying propagation characteristics [3], etc.) However, it is not trivial to extend these results for functions of higher degrees and even for cubic functions. It is important to understand how the properties behave for the different degrees of functions.