Paper 2011/290 Original: eprint.iacr.org/2011/290 ↗

Some Results Concerning Generalized Bent Functions

Abstract

In this paper we investigate the properties of generalized bent functions defined on $\BBZ_2^n$ with values in $\BBZ_q$ where $q \ge 2$ is any positive integer. We characterize the class of generalized bent functions symmetric with respect to two variables, provide an analogue of Maiorana--McFarland type bent functions in the generalized set up. A class of bent functions called generalized spreads type is introduced and it is demonstrated that recently introduced Dillon type generalized bent functions and Maiorana--McFarland type generalized bent functions can be described as generalized spreads type functions. Thus unification of two different types of generalized bent functions is achieved.