Equivalence for generalized Boolean functions

Abstract

Equivalence plays a key-role for the classification of functions between elementary abelian groups V(p) n and V(p) k . One distinguishes between affine equivalence, extended affine (EA) equivalence, and the most general CCZ-equivalence. Recently, there has been an increased interest in functions from elementary abelian groups V(p) n to cyclic groups Zpk . We initiate the study of equivalence for functions from V(p) n to Zpk . We show that CCZequivalence is more general than EA-equivalence. For some classes of functions, CCZ-equivalence reduces to EA-equivalence. We show that CCZ-equivalence between two functions from V(p) n to Zpk implies CCZ-equivalence of two associated vectorial functions from V(p) n to V(p) k .