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arXiv · 2002.01867

On existence of some special pair of primitive elements over finite fields

C. Carvalho·J. P. G. Sousa·V. G. L. Neumann·G. Tizziotti
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Abstract

In this paper we generalize the results of Sharma, Awasthi and Gupta (see \cite{SAG}). We work over a field of any characteristic with $q = p^k$ elements and we give a sufficient condition for the existence of a primitive element $\alpha \in \mathbb{F}_{p^k}$ such that $f(\alpha)$ is also primitive in $\mathbb{F}_{p^k}$, where $f(x) \in \mathbb{F}_{p^k}(x)$ is a quotient of polynomials with some restrictions. We explicitly determine the values of $k$ for which such a pair exists for $p=2,3,5$ and $7$.

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C. Carvalho, J. P. G. Sousa, V. G. L. Neumann, G. Tizziotti. 2020-02-05. On existence of some special pair of primitive elements over finite fields. https://arxiv.org/abs/2002.01867

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