# 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}
}
• Published 2018
• Physics, Mathematics, Computer Science
• Finite Fields Their Appl.
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
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