On Vectorial Bent Property Of A Class Of Trace Trinomial Vectorial Boolean Functions

Bent functions have wide applications in cryptology,combinatorial mathematics and coding theory.Recently,a series of important research results on Bent func-tions have been obtained.In this thesis,we mainly considers the vectorial Bent property of the trace trinomial function F(x)=Trk2k(x2k-1+x3(2k-1)+?zxr(2k-1)(??F22k*,?2k+1=1,z?F2k*,k?2,r>3 odd).For the case r|2k+1,we prove that F is not vectorial Bent.For the case r |2k+1,by using Lucas formula and group structure of finite field,we completely determine the vectorial Bent property of F when r = 7 and r = 9.