A Construction of Bent Functions on a finite group

TL;DR

This paper investigates the conditions under which class functions on finite groups, especially cyclic groups, are bent functions, providing necessary and sufficient criteria for their construction.

Contribution

It introduces new necessary and sufficient conditions for class functions on finite abelian and cyclic groups to be bent functions.

Findings

Necessary condition for abelian groups

Necessary and sufficient condition for cyclic groups

Framework for constructing bent functions on finite groups

Abstract

In this paper, we discuss when a class function on a finite group is a bent function. We have found a necessary condition for a class function on a finite abelian group to be bent. Also, we have found a necessary and sufficient condition for a class function on a finite cyclic group to be bent.