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Dual bent functions on finite groups and $$C$$-algebras. (English) Zbl 1327.43004
Summary: 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.

##### MSC:
 43A30 Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. 20C99 Representation theory of groups 11T71 Algebraic coding theory; cryptography (number-theoretic aspects)
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