Affine equivalence classes of 2-rotation symmetric cubic Boolean functions. Issue 3 (3rd July 2018) - Reid, Elizabeth M.; Cusick, Thomas W.
ABSTRACT: A Boolean function in variables that is generated by applying all even powers of the cyclic permutation of the variables to a single cubic monomial is called a cubic monomial rotation symmetric 2-function (or cubic 2-MRS function for short). In 2015, Cusick and Johns gave a complete description of the affine equivalence classes for such functions with generating monomial with 1< r < s and r and s not both odd. In this paper we develop the theory further by determining the smallest sets that act on the set of all these cubic 2-MRS functions to give the affine equivalence classes. Also, suppose f and g are two of these functions such that there exists a permutation σ of the variables where We give a complete description of all such permutations σ and an exact count of their number.