On a class of permutation polynomials and their inverses

Abstract

We introduce a class of permutation polynomial over $F_{q^n}$ that can be written in the form $\frac{L\left(x\right)}{x^{q+1}}$ or $\frac{L\left(x^{q+1}\right)}{x}$ for some q-linear polynomial L over $F_{q^n}$. Specifically, we present those permutation polynomials explicitly as well as their inverses. In addition, more permutation polynomials can be derived in a more general form.