Existence of primitive k-normal elements for critical values over finite fields

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

Let ${\mathbb{F}}_{q^n}$ be a finite field with $q^n$ elements. An element $\hat{I}\pm \in {\mathbb{F}}_{q^n}$ is called $k$-normal over ${\mathbb{F}}_q$ if $\hat{I}\pm$ and its conjugates generate a vec…