Equivalence for generalized boolean functions

Official URL: https://dx.doi.org/10.3934/amc.2023009

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 CCZ-equivalence 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 Vn(p) to ℤpk implies CCZ-equivalence of two associated vectorial functions from V(p) n to V(p) k..