A class of new permutation trinomials

In this paper, we characterize the coefficients of f(x)=x+a1xq(q−1)+1+a2x2(q−1)+1 in Fq2[x] for even q that lead f(x) to be a permutation of Fq2. We transform the problem into studying some low-degree equations with variable in the unit circle, which are intensively investigated with some parameterization techniques. From the numerical results, the coefficients that lead f(x) to be a permutation appear to be completely characterized in this paper. It is also demonstrated that some permutations proposed in this paper are quasi-multiplicative (QM) inequivalent to the previously known permutation trinomials.