In this paper we introduce generalized hyperbent functions from F2n to
Z2k, and investigate decompositions of generalized (hyper)bent functions.
We show that generalized (hyper)bent functions from F2n to Z2k
consist of components which are generalized (hyper)bent functions from
F2n to Z2k′ for some k′<k. For odd n, we show
that the Boolean functions associated to a generalized bent function form an
affine space of semibent functions. This complements a recent result for even
n, where the associated Boolean functions are bent.Comment: 24 page