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arXiv · 1903.03160

The trace of 2-primitive elements of finite fields (amended version)

Stephen D. Cohen·Giorgos Kapetanakis
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Abstract

Let $q$ be a prime power and $n, r$ integers such that $r\mid q^n-1$. An element of $\mathbb{F}_{q^n}$ of multiplicative order $(q^n-1)/r$ is called \emph{$r$-primitive}. For any odd prime power $q$, we show that there exists a $2$-primitive element of $\mathbb{F}_{q^n}$ with arbitrarily prescribed $\mathbb{F}_q$ trace when $n\geq 3$. Also we explicitly describe the values that the trace of such elements may have when $n=2$. A feature of this amended version is the reduction of the discussion to extensions of prime degree $n$.

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Stephen D. Cohen, Giorgos Kapetanakis. 2019-03-07. The trace of 2-primitive elements of finite fields (amended version). https://arxiv.org/abs/1903.03160

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