Existence of primitive $1$-normal elements in finite fields

Lucas Reis, David Thomson

An element $\alpha \in {\mathbb{F}}_{q^n}$ is \emph{normal} if $\mathcal{B}=\{\alpha ,{\alpha }^q,\dots ,{\alpha }^{q^{n-1}}\}$ forms a basis of ${\mathbb{F}}_{q^n}$ as a vector space over ${\mathbb{F}}_q$; in…