Permutation Polynomials of the form ${\mathtt{X}}^r(a+{\mathtt{X}}^{2(q-1)})$ --- A Nonexistence Result

Xiang-dong Hou

Let $f={\mathtt{X}}^r(a+{\mathtt{X}}^{2(q-1)})\in {\mathbb{F}}_{q^2}[\mathtt{X}]$, where $a\in {\mathbb{F}}_{q^2}^{\ast }$ and $r\ge 1$. The parameters $(q,r,a)$ for which $f$ is a permutation polynomial (PP)…