论文标题
$ x^r（x^{q-1}+a）$ \ $ \ mathbb f_ {q^e} $上的置换二项式
Permutation binomials of the form $x^r(x^{q-1}+a)$ over $\mathbb F_{q^e}$
论文作者
论文摘要
我们介绍了$ x^r（x^{q-1}+a）$的置换二项式的几个存在和不存在的结果，其中$ e \ geq 2 $和$ a \ in \ mathbb {f} _ {q^e}^*$。结果，我们获得了$ \ Mathbb {f} _ {q^2} $，$ \ MATHBB {f} _ {q^3} $，$ \ MATHBB {f} _ $ \ mathbb {f} _ {p^6} $，其中$ p $是一个奇怪的素数。
We present several existence and nonexistence results for permutation binomials of the form $x^r(x^{q-1}+a)$, where $e\geq 2$ and $a\in \mathbb{F}_{q^e}^*$. As a consequence, we obtain a complete characterization of such permutation binomials over $\mathbb{F}_{q^2}$, $\mathbb{F}_{q^3}$, $\mathbb{F}_{q^4}$, $\mathbb{F}_{p^5}$, and $\mathbb{F}_{p^6}$, where $p$ is an odd prime.
