Inverse of large class of permutation polynomials of finite fields
Yanbin Zheng · 2018
It is known that $x(x^{s} -a)^{(q^m - 1)/s}$ with $a \in \mathbb{F}_{q^n}^{*}$ is a permutation polynomial of $\mathbb{F}_{q^n}$ if and only if $a$ is not a $s$-th power of an element of $\mathbb{F}_{q^n}^{*}$. In this paper, the inverse of $f(x)$ on $\mathbb{F}_{q^n}$ is presented. In particular, explicit expressions of inverses of $x(x^2 -a)^2$, $x(x^3 -a)^2$ and $x(x^2 -a)^3$ are given.