Existence results on $k$-normal elements over finite fields
Existence results on $k$-normal elements over finite fields
An element \alpha \in \mathbb{F}_{q^n} is normal over \mathbb{F}_q if \alpha and its conjugates \alpha, \alpha^q, \dots, \alpha^{q^{n-1}} form a basis of \mathbb{F}_{q^n} over \mathbb{F}_q . In 2013, Huczynska, Mullen, Panario and Thomson introduced the concept of k -normal elements, generalizing the normal elements. In the past few years, many …