Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Permutation binomials of the form $x^r(x^{q-1}+a)$ over $\mathbb
  F_{q^e}$   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.

35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an