Several Classes Of Permutation Polynomials With Special Form

Suppose that q is a power of a prime,Fq is a finite field with q elements.Any map-ping from a finite field Fq into itself can be represented by a polynomial on Fq.If the polynomial f(x)? Fq[x]is a one-to-one mapping from Fq to itself,it is said that f(x)is a permutation polynomial on Fq.Permutation polynomials on finite fields have impor-tant applications in cryptography,coding,combinatorial design and so on.Therefore,studying the construction and properties of permutation polynomials on finite fields is not only of theoretical significance,but also of important application value.Permutation polynomials over finite fields have been studied for a long time.In recent years,people have paid great attention to the construction and analysis of per-mutation polynomials with special structures or concise expressions.In particular,a lot of research results have been obtained on the form of xrf(xpm-1/d)permutation poly-nomials.In this paper,we continue to study some permutation polynomials with this form on Fq2.The main conclusions are as follows:(1)Two classes of permutation polynomials with the form x + xs(2m-1)+1 + xt(2m-1)+1 over the finite field F22m,their parameters are:·(s,t)=(2/7,8/7),gcd(2,m)=1;·(s,,t)=(-2/7,8/7),m?2,4 mod 6.In the process of proving the permutation of the above polynomials,we obtain a new method of constructing permutation polynomials from known permutation polynomi-als.(2)One class of permutation polynomials with the form x4q-3+xq2-2q+2-x over the finite field F32m and m(?)0(mod 6).