Abstract
Recently in Çeşmelioğlu, Meidl (Adv. Math. Commun., 18, 2024), the study of EA-equivalence and CCZ-equivalence for functions from Vn(p) to the cyclic group Zpk has been initiated, where Vn(p) denotes an n-dimensional vector space over Fp . Amongst others it has been shown that there exist functions from Vn(2) to Z4 which are CCZ-equivalent but not EA-equivalent. We extend these results to larger classes of functions from Vn(p) to Zpk . We then discuss constructions of generalized bent functions from Vn(p) to Zpk , p odd or p = 2 and n is even, which correspond to large affine spaces of bent functions. In particular we employ versions of the direct sum, the semi-direct sum and of a recent secondary bent function construction in Wang et. al., (IEEE Trans. Inform. Theory 69, 2023), to generate large affine spaces of bent functions. Finally we present a solution for constructing generalized bent functions from Vn(2) to Z2k , n odd, from arbitrary generalized bent functions from Vn-1(2) to Z2k-1 .