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arXiv · 1701.05643

A note on primitive $1-$normal elements over finite fields

Lucas Reis
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Abstract

Let $q$ be a prime power of a prime $p$, $n$ a positive integer and $\mathbb F_{q^n}$ the finite field with $q^n$ elements. The $k-$normal elements over finite fields were introduced and characterized by Huczynska et al (2013). Under the condition that $n$ is not divisible by $p$, they obtained an existence result on primitive $1-$normal elements of $\mathbb F_{q^n}$ over $\mathbb F_q$ for $q>2$. In this note, we extend their result to the excluded case $q=2$.

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Lucas Reis. 2017-01-19. A note on primitive $1-$normal elements over finite fields. https://arxiv.org/abs/1701.05643

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