Complete characterization of generalized bent and 2^k-bent Boolean functions

In this paper we investigate properties of generalized bent Boolean functions and 2k-bent (i.e., negabent, octabent, hex- adecabent, et al.) Boolean functions in a uniform framework. We generalize the work of Stˇ anicˇ a et al., present necessary and sufficient conditions for generalized bent Boolean functions and 2k-bent Boolean functions in terms of classical bent functions, and completely characterize these functions in a combinatorial form. The result of this paper further shows that all generalized bent Boolean functions are regular

On weak and strong 2k-bent Boolean functions

In this paper we introduce a sequence of discrete Fourier trans- forms and de ne new versions of bent functions, which we shall call (weak, strong) octa/hexa/2k-bent functions. We investigate relation- ships between these classes and completely characterize the octabent and hexabent functions in terms of bent functions