Primitive element pairs with a prescribed trace in the cubic extension of a finite field
| Autor: | Booker, Andrew R., Cohen, Stephen D., Leong, Nicol, Trudgian, Tim |
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| Rok vydání: | 2022 |
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| Druh dokumentu: | Working Paper |
| Popis: | We prove that for any prime power $q\notin\{3,4,5\}$, the cubic extension $\mathbb{F}_{q^3}$ of the finite field $\mathbb{F}_q$ contains a primitive element $\xi$ such that $\xi+\xi^{-1}$ is also primitive, and $\textrm{Tr}_{\mathbb{F}_{q^3}/\mathbb{F}_q}(\xi)=a$ for any prescribed $a\in\mathbb{F}_q$. This completes the proof of a conjecture of Gupta, Sharma, and Cohen concerning the analogous problem over an extension of arbitrary degree $n\ge3$. Comment: 4 pages |
| Databáze: | arXiv |
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