an:06686332
Zbl 1358.43004
Fan, Yun; Xu, Bangteng
Fourier transforms and bent functions on faithful actions of finite abelian groups
EN
Des. Codes Cryptography 82, No. 3, 543-558 (2017).
00362825
2017
j
43A25 11T71 20C99
group actions; \(G\)-linear functions; \(G\)-dual sets; Fourier transforms on \(G\)-sets; bent functions; perfect nonlinear functions
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.
George Stoica (Saint John)