Generalized Bent Functions and Perfect Nonlinear Functions over Finite Fields

作     者：Jihong Teng Xiaoying Huang Zhibo Lu Department of mathematics and physics Zhengzhou Information Engineering University Zhengzhou China 

会议名称：《2011 IEEE International Conference on Information Theory and Information Security(ICITIS 2011)》

会议日期：2011年

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by NSFC(60803154) 

关 键 词：Finite Field perfect nonlinear function Bent funcion generalized Bent function vector Bent function Chrestenson cycle spectra autocorrelation function 

摘      要：In this paper,we firstly introduce some equivalent definitions of generalized Bent functions and perfect nonlinear functions over finite field,which indicate that generalized Bent functions and perfect nonlinear functions are quite *** the relationships of generalized Bent functions over finite field and generalized Bent functions over its prime field are suggested,as well as that of perfect nonlinear functions over finite field and vector generalized Bent functions over its prime field,which enable us to investigate the existence and constructions of perfect nonlinear functions over finite field through the vector Bent functions over the prime field.