On elements of high order in general finite fields
We show that the Gao's construction gives for any finite field \(F_{q^{n}}\) elements with the multiplicative order at least \(\binom{n+t-1}{t}\prod _{i=0}^{t-1}\frac{1}{d^{i}}\), where \(d=\left\lceil 2\log _{q} n\right\rceil\), \(\;t=\left\lfloor \log _{d} n\right\rfloor\).
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| Date: | 2018 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2018
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1062 |
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| Journal Title: | Algebra and Discrete Mathematics |