Effective existence of primitive k-normal elements via affine spaces

Josimar J. R. Aguirre, Sarah F. M. Mazzini, Victor G. L. Neumann

Let ${\mathbb{F}}_{q^n}$ be the finite field with $q^n$ elements. An element $\alpha \in {\mathbb{F}}_{q^n}$ is $k$-normal over ${\mathbb{F}}_q$ if $\alpha$ and its conjugates span an $\mathbb{F}_q…