Complete Characterization of Generalized Bent and 2k-Bent Boolean Functions

In this paper we investigate properties of generalized bent Boolean functions and 2-bent (i.e., negabent, octabent, hexadecabent, et al.) Boolean functions in a uniform framework. We generalize the work of Stǎnicǎ et al., present necessary and sufficient conditions for generalized bent Boolean functions and 2-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. Index Terms Boolean functions, Walsh-Hadamard transforms, 2-bent functions, generalized bent functions, cyclotomic fields