In a recent paper Zhang et al. constructed 17 families of permutation pentanomials of the form $x^t+x^{r_1(q-1)+t}+x^{r_2(q-1)+t}+x^{r_3(q-1)+t}+x^{r_4(q-1)+t}$ over $\mathbb{F}_{q^2}$ where $q=2^m$. In this paper for 14 of these 17 families we provide a simple explanation as to why they are permutations. We also extend these 14 families into three general classes of permutation pentanomials over $\mathbb{F}_{q^2}$.

翻译：在最近的一篇论文中，Zhang 等人构造了 17 族形如 $x^t+x^{r_1(q-1)+t}+x^{r_2(q-1)+t}+x^{r_3(q-1)+t}+x^{r_4(q-1)+t}$ 的置换五项式，其中定义在 $\mathbb{F}_{q^2}$ 上且 $q=2^m$。本文针对这 17 族中的 14 族，给出了它们为何是置换多项式的一个简明解释。我们还将这 14 族推广为 $\mathbb{F}_{q^2}$ 上的三类广义置换五项式。