A conjecture on permutation trinomials over finite fields of characteristic two

Abstract

In this paper, by analyzing the quadratic factors of an \begin{document}$ 11 $\end{document} -th degree polynomial over the finite field \begin{document}$ {\mathbb F}_{2^n} $\end{document} , a conjecture on permutation trinomials over \begin{document}$ {\mathbb F}_{2^n}[x] $\end{document} proposed very recently by Deng and Zheng is settled, where \begin{document}$ n = 2m $\end{document} and \begin{document}$ m $\end{document} is a positive integer with \begin{document}$ \gcd(m,5) = 1 $\end{document} .