Decomposing generalized bent and hyperbent functions

Abstract

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.Second author is supported by the Austrian Science Fund (FWF)Project number. M 1767-N2