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arXiv · 2412.08455

Existence of Special Types Primitive Pairs in Finite Fields Avoiding Affine Hyperplanes

Himangshu Hazarika·Giorgos Kapetanakis·Dhiren Kumar Basnet
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Abstract

Let $\Fm$ be finite fields of order $q^m$, where $m\geq 2$ and $q$, a prime power. Given $\F$-affine hyperplanes $A_1,\ldots, A_m$ of $\Fm$ in general position, we study the existence of primitive element $α$ of $\Fm$, such that $f(α)$ is also primitive, where $ax^2+bx+c\in \Fm[x]$ ($a\neq 0$ and $b^2\neq 4ac$) in $\Fm$ and the primitive pair $(α, f(α))$ avoids each $A_i$. We establish results for fields of higher order.

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Himangshu Hazarika, Giorgos Kapetanakis, Dhiren Kumar Basnet. 2024-12-11. Existence of Special Types Primitive Pairs in Finite Fields Avoiding Affine Hyperplanes. https://arxiv.org/abs/2412.08455

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