Construction of Negabent Function Based on Trace Function over Finite Field
Negabent function is a Boolean function with optimal autocorrelation and high nonlinearity,which has been widely used in cryptography,coding theory and combination design.In this paper,by combining trace function on a finite field with permutation polynomials,two methods for constructing negabent functions are proposed.Both the two kinds of constructed negabent functions take on such form:Trk1(λx2k+1)+ Trn1(ux)Trn1(vx)+Trn1(mx)Trn1(dx).In the first construction method,negabent functions can be obtained by adjusting the three parameters inλ,u,v,m.In particular,whenλ≠1,(2n-1-2)(2n-1)(2n-4)negabent functions can be obtained.In the second construction method,negabent functions can be obtained by adjusting the four parameters in λ,u,v,m,d.In particular,whenλ≠1,at least2n-1[(2n-1-2)(2n-1-3)+ 2n-1-4]negabent functions can be obtained.
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