Existence of Special Types Primitive Pairs in Finite Fields Avoiding Affine Hyperplanes
| Autor: | Hazarika, Himangshu, Kapetanakis, Giorgos, Basnet, Dhiren Kumar |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $\alpha$ of $\Fm$, such that $f(\alpha)$ 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 $(\alpha, f(\alpha))$ avoids each $A_i$. We establish results for fields of higher order. Comment: 12 pages |
| Databáze: | arXiv |
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