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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| Language: | English |
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Lugansk National Taras Shevchenko University
2018
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1062 |
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| Journal Title: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-10622018-04-26T02:40:33Z On elements of high order in general finite fields Popovych, Roman finite field, multiplicative order, Diophantine inequality 11T30 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 \(d=\left\lceil 2\log _{q} n\right\rceil\), \(\;t=\left\lfloor \log _{d} n\right\rfloor\). Lugansk National Taras Shevchenko University 2018-04-26 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1062 Algebra and Discrete Mathematics; Vol 18, No 2 (2014) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1062/584 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2018-04-26T02:40:33Z |
| collection |
OJS |
| language |
English |
| topic |
finite field multiplicative order Diophantine inequality 11T30 |
| spellingShingle |
finite field multiplicative order Diophantine inequality 11T30 Popovych, Roman On elements of high order in general finite fields |
| topic_facet |
finite field multiplicative order Diophantine inequality 11T30 |
| format |
Article |
| author |
Popovych, Roman |
| author_facet |
Popovych, Roman |
| author_sort |
Popovych, Roman |
| title |
On elements of high order in general finite fields |
| title_short |
On elements of high order in general finite fields |
| title_full |
On elements of high order in general finite fields |
| title_fullStr |
On elements of high order in general finite fields |
| title_full_unstemmed |
On elements of high order in general finite fields |
| title_sort |
on elements of high order in general finite fields |
| description |
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 \(d=\left\lceil 2\log _{q} n\right\rceil\), \(\;t=\left\lfloor \log _{d} n\right\rfloor\). |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1062 |
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AT popovychroman onelementsofhighorderingeneralfinitefields |
| first_indexed |
2025-07-17T10:30:49Z |
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2025-07-17T10:30:49Z |
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1837890130431442944 |