About $r$- primitive and $k$-normal elements in finite fields

Cícero Carvalho, Josimar J. R. Aguirre, Victor G. L. Neumann

In 2013, Huczynska, Mullen, Panario and Thomson introduced the concept of $k$-normal elements: an element $\alpha \in {\mathbb{F}}_{q^n}$ is $k$-normal over ${\mathbb{F}}_q$ if the greatest…