Some specific classes of permutation polynomials over $ {\textbf{F}}_{q^3} $

Abstract

<abstract><p>Constructing permutation polynomials is a hot topic in finite fields. Recently, huge kinds of permutation polynomials over $ {\bf F}_{q^2} $ have been studied. In this paper, by using AGW criterion and piecewise method, we construct several classes of permutation polynomials over $ {\bf F}_{q^3} $ of the forms similar to $ (x^{q^2}+x^q+x+\delta)^{\frac{q^{3}-1}{d}+1}+L(x) $, for $ d = 2, 3, 4, 6, $ where $ L(x) $ is a linearized polynomial over $ {\bf F}_{q} $.</p></abstract>