Existence of primitive 1-normal elements in finite fields

@article{Reis2018ExistenceOP,
  title={Existence of primitive 1-normal elements in finite fields},
  author={Lucas Reis and D. Thomson},
  journal={Finite Fields Their Appl.},
  year={2018},
  volume={51},
  pages={238-269}
}
An element $\alpha \in \mathbb F_{q^n}$ is \emph{normal} if $\mathcal{B} = \{\alpha, \alpha^q, \ldots, \alpha^{q^{n-1}}\}$ forms a basis of $\mathbb F_{q^n}$ as a vector space over $\mathbb F_{q}$; in this case, $\mathcal{B}$ is a normal basis of $\mathbb F_{q^n}$ over $\mathbb F_{q}$. The notion of $k$-normal elements was introduced in Huczynska et al (2013). Using the same notation as before, $\alpha$ is $k$-normal if $\mathcal{B}$ spans a co-dimension $k$ subspace of $\mathbb F_{q^n}$. It… Expand
Existence results on k-normal elements over finite fields
A note on depth-$b$ normal elements
Character sums over affine spaces and applications
Variations of the Primitive Normal Basis Theorem
On $k$-normal elements over finite fields
Existence and Cardinality of k-Normal Elements in Finite Fields
N T ] 1 9 O ct 2 01 7 On k-normal elements over finite fields
Existence of primitive 2-normal elements in finite fields

References

SHOWING 1-10 OF 13 REFERENCES
Primitive Normal Bases with Prescribed Trace
Existence and properties of k-normal elements over finite fields
Primitive roots in a finite field
Contributions to the theory of finite fields
Pairs of primitive elements in fields of even order
Primitive elements and polynomials with arbitrary trace
...
1
2
...