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Fourier transforms and bent functions on faithful actions of finite abelian groups. (English) Zbl 1358.43004
Let $$G$$ be a finite abelian group acting faithfully on a finite set $$X$$.The authors are concerned with the Fourier analysis on $$X$$, as a generalization of the classical Fourier analysis on $$G$$. The former is used to study the bentness and perfect nonlinearity of functions on $$X$$ by their own Fourier transforms on the $$G$$-dual set of $$X$$. Illustrative examples complete the study.

MSC:
 43A25 Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups 11T71 Algebraic coding theory; cryptography (number-theoretic aspects) 20C99 Representation theory of groups
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