Decomposing Generalized Bent and Hyperbent Functions
Thor Martinsen, Wilfried Meidl, Sihem Mesnager, Pantelimon Stănică · IEEE Transactions on Information Theory · 2017
In this paper, we introduce generalized hyperbent functions from F2nto ℤ2k, and investigate decompositions of generalized (hyper)bent functions. We show that generalized (hyper)bent functions f from F2nto ℤ2kconsist of components which are generalized (hyper)bent functions from F2ntoZ2k'for some k' <; k. For even n, most notably we show that the g-hyperbentness of f is equivalent to the hyperbentness of the components of f with some conditions on the Walsh-Hadamard coefficients. 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.