Abstract:We give the equivalence between perfect nonlinear functions and appropriate splitting semi-regular relative difference sets, construct a class of splitting relative difference sets by using Galois rings and bent functions, and prove that there exists a 4-phase perfect nonlinear function if and only if the number of input variables is at least twice the number of output variables. # 2005 Wiley Periodicals, Inc. J Combin Designs 13: [349][350][351][352][353][354][355][356][357][358][359][360][361][362] 2005

No abstract

No abstract

No abstract

No abstract

No abstract

No abstract

No abstract