Generalized bent Boolean functions and strongly regular Cayley graphs

Abstract

In this paper we define the (edge-weighted) Cayley graph associated to a generalized Boolean function, introduce a notion of strong regularity and give several of its properties. We show some connections between this concept and generalized bent functions (gbent), that is, functions with flat Walsh-Hadamard spectrum. In particular, we find a complete characterization of quartic gbent functions in terms of the strong regularity of their associated Cayley graph.

On some properties of self-dual bent functions

“…In [11,21,12,34] different constructions and properties of generalized bent functions were obtained. The connection between concepts of strong regularity of (edge-weighted) Cayley graph associated to a generalized Boolean function and gbent functions was pointed in [28]. The complete characterization of generalized bent functions from different perspectives was recently presented in [13,35,25].…”