New results on permutation polynomials over finite fields

Abstract

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 $L(x)+{\sum }_{j=1}^k{\gamma }_j{h}_j(f_j(x))$ and $x+{\sum }_{j=1}^k{\gamma }_j{f}_j(x)$. These generalize the results obtained by Kyureghyan in 2011. Consequently, we characterize permutation polynomials of the form $L(x)+{\sum }_{i=1}^l{\gamma }_i{\mathrm{Tr}}_{{\mathbf{F}}_{q^m}/{\mathbf{F}}_q}(h_i(x))$, which extends a theorem of Charpin and Kyureghyan obtained in 2009.

11 pages. To appear in International Journal of Number Theory

References in corpus (2)

• Permutation polynomials on F_q induced from bijective Redei functions on subgroups of the multiplicative group of F_q
• Permutation polynomials induced from permutations of subfields, and some complete sets of mutually orthogonal latin squares