Dual bent functions on finite groups and C-algebras

Abstract

The dual of a (bent) function on a finite abelian group is a natural concept. In this paper we study the dual bent functions on finite nonabelian groups. A more general algebraic structure of a C-algebra provides a better and natural context for this purpose. We will first study Fourier transforms, bent functions, and dual bent functions on C-algebras. Then as an application, we obtain the properties of dual bent functions on finite nonabelian groups. Examples of bent functions on C-algebras are also presented.