Some new forms of permutation polynomials over finite fields with even characteristic

Let q=2m. In this paper, we propose several classes of permutation polynomials of the forms L1(xd1)k1+L2(xd2)k2, L1(xd1)k1+L3(xd2+xd3)k2 over Fq2 and L1(xd1)+L3(c1xd2+c2xd3) over Fq3 from certain linearized polynomials L1(x)=x+a0xq,L2(x)=b0x+b1xq,L3(x)=x+xq. The numerical results suggest that the sufficient conditions we find in the first class of permutation polynomials (see Theorem 3.2) are also necessary. Some known results on permutation polynomials over Fq2 are covered by ours.