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arXiv · 1904.00443

Primitive Element Pairs with a Prescribed Trace in the Quartic Extension of a Finite Field

Stephen D. Cohen·Anju Gupta
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Abstract

In this article, we give a largely self-contained proof that the quartic extension $\mathbb{F}_{q^4}$ of the finite field $\mathbb{F}_q$ contains a primitive element $\alpha $ such that the element $\alpha+\alpha^{-1}$ is also a primitive element of ${\mathbb{F}_{q^4}},$ and $Tr_{\mathbb{F}_{q^4}|\mathbb{F}_{q}}(\alpha)=a$ for any prescribed $a \in \mathbb{F}_q$. The corresponding result for finite field extensions of degrees exceeding 4 has already been established by Gupta, Sharma and Cohen.

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Stephen D. Cohen, Anju Gupta. 2019-03-31. Primitive Element Pairs with a Prescribed Trace in the Quartic Extension of a Finite Field. https://doi.org/10.1142/s0219498821501681

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