  In this paper, we get several new results on permutation polynomials over
finite fields. First, by using the linear translator, we construct permutation
polynomials of the forms $L(x)+\sum_{j=1}^k \gamma_jh_j(f_j(x))$ and
$x+\sum_{j=1}^k\gamma_jf_j(x)$. These generalize the results obtained by
Kyureghyan in 2011. Consequently, we characterize permutation polynomials of
the form $L(x)+\sum_{i=1} ^l\gamma_i {\rm Tr}_{{\bf F}_{q^m}/{\bf
F}_{q}}(h_i(x))$, which extends a theorem of Charpin and Kyureghyan obtained in
2009.
