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arXiv · 1709.03141

On the existence of primitive completely normal bases of finite fields

Theodoulos Garefalakis·Giorgos Kapetanakis
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Abstract

Let $\mathbb{F}_q$ be the finite field of characteristic $p$ with $q$ elements and $\mathbb{F}_{q^n}$ its extension of degree $n$. We prove that there exists a primitive element of $\mathbb{F}_{q^n}$ that produces a completely normal basis of $\mathbb{F}_{q^n}$ over $\mathbb{F}_q$, provided that $n=p^{\ell}m$ with $(m,p)=1$ and $q>m$.

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Theodoulos Garefalakis, Giorgos Kapetanakis. 2017-09-10. On the existence of primitive completely normal bases of finite fields. https://arxiv.org/abs/1709.03141

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