Further results on permutation polynomials via linear translators

In this paper, by using linear translators, we characterize a new class of permutation polynomials of the form x + Sigma(k)(i=1)gamma(i)h(i)(fi(x)), which has a more general form than x +gamma h(f(x)). Then, we present the compositional inverses of such permutation polyno- mials. Furthermore, by specifying the functions h(i)(x) and f(i)(x), we can get some new permutation polynomials of the forms x + gamma(1)(Tr(beta(1)x)+delta(1))(s1) + gamma(2) (Tr(beta(2)x) + delta(2))(s2) and x+gamma(1)(Tr(x)+delta)(s)(1)+gamma(2)(Tr(x)+delta(2))(s2), where Tr(x) is the trace function.