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 |
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Algebra and Discrete Mathematics| _version_ | 1875384740703371264 |
|---|---|
| author | Popovych, R. |
| author_facet | Popovych, R. |
| author_sort | Popovych, R. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-04-26T02:40:33Z |
| 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 \(d=\left\lceil 2\log _{q} n\right\rceil\), \(\;t=\left\lfloor \log _{d} n\right\rfloor\). |
| first_indexed | 2026-02-08T07:57:33Z |
| format | Article |
| id | admjournalluguniveduua-article-1062 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T07:57:33Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spellingShingle | finite field multiplicative order Diophantine inequality 11T30 Popovych, R. On elements of high order in general finite fields |
| title | 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_short | On elements of high order in general finite fields |
| title_sort | on elements of high order in general finite fields |
| topic | finite field multiplicative order Diophantine inequality 11T30 |
| topic_facet | finite field multiplicative order Diophantine inequality 11T30 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1062 |
| work_keys_str_mv | AT popovychroman onelementsofhighorderingeneralfinitefields |