A complete classification of permutation binomials of the form $X^r(X^{q-1}+a)$ over finite fields
Year: 2026
Type: preprint
Abstract: We classify, for every prime power $q$ and every $e\geqslant2$, the permutation binomials $X^r(X^{q-1}+a)$ over $\mathbb F_{q^e}$. Writing $\ell_j(q)=(q^j-1)/(q-1)$, such a binomial is a permutation if and only if $\gcd(r,q-1)=1$, $(-a)^{\ell_e(q)}\ne1$, and $r\ell_h(q)\equiv1\pmod{\ell_e(q)}$ for some $1\leqslant h
Source: arXiv (Cornell University)
Author: Fan, Xiang
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G7532033765
OpenAlex ID: W7213602794