期刊论文

Xu, Bangteng

英文

DESIGNS CODES AND CRYPTOGRAPHY

0925-1022

2017

82

3

543-558

10.1007/s10623-016-0177-8

This work was done while the first author was visiting the second author at Eastern Kentucky University in Spring 2014; he is grateful for the hospitality. The work of the first author is supported by NSFC with Grant Number 11271005. The authors would like to thank the referees for their useful comments, especially for the suggestions of Theorem and Example .

本校为第一机构

Let G be a finite abelian group acting faithfully on a finite set X. The G-bentness and G-perfect nonlinearity of functions on X are studied by Poinsot and co-authors (Discret Appl Math 157:1848–1857, 2009; GESTS Int Trans Comput Sci Eng 12:1–14, 2005) via Fourier transforms of functions on G. In this paper we introduce the so-called G-dual set X^ of X, which plays the role similar to the dual group G^ of G, and develop a Fourier analysis on X, a generalization of the Fourier analysis on the group G. Then we characterize the bentness and perf...