Normal high order elements in finite field extensions based on the cyclotomic polynomials
We consider elements which are both of high multiplicative order and normal in extensions \(F_{q^{m} } \) of the field \(F_{q} \). If the extension is defined by a cyclotomic polynomial, we construct such elements explicitly and give explicit lower bounds on their orders.
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| Date: | 2020 |
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| Format: | Article |
| Language: | English |
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Lugansk National Taras Shevchenko University
2020
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1117 |
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| Journal Title: | Algebra and Discrete Mathematics |
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admjournalluguniveduua-article-11172020-07-08T07:13:20Z Normal high order elements in finite field extensions based on the cyclotomic polynomials Popovych, R. Skuratovskii, R. finite field, cyclotomic polynomial, normal basis, high multiplicative order element 11T30 We consider elements which are both of high multiplicative order and normal in extensions \(F_{q^{m} } \) of the field \(F_{q} \). If the extension is defined by a cyclotomic polynomial, we construct such elements explicitly and give explicit lower bounds on their orders. Lugansk National Taras Shevchenko University 2020-07-08 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1117 10.12958/adm1117 Algebra and Discrete Mathematics; Vol 29, No 2 (2020) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1117/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1117/347 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1117/547 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1117/548 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1117/549 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1117/552 Copyright (c) 2020 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2020-07-08T07:13:20Z |
| collection |
OJS |
| language |
English |
| topic |
finite field cyclotomic polynomial normal basis high multiplicative order element 11T30 |
| spellingShingle |
finite field cyclotomic polynomial normal basis high multiplicative order element 11T30 Popovych, R. Skuratovskii, R. Normal high order elements in finite field extensions based on the cyclotomic polynomials |
| topic_facet |
finite field cyclotomic polynomial normal basis high multiplicative order element 11T30 |
| format |
Article |
| author |
Popovych, R. Skuratovskii, R. |
| author_facet |
Popovych, R. Skuratovskii, R. |
| author_sort |
Popovych, R. |
| title |
Normal high order elements in finite field extensions based on the cyclotomic polynomials |
| title_short |
Normal high order elements in finite field extensions based on the cyclotomic polynomials |
| title_full |
Normal high order elements in finite field extensions based on the cyclotomic polynomials |
| title_fullStr |
Normal high order elements in finite field extensions based on the cyclotomic polynomials |
| title_full_unstemmed |
Normal high order elements in finite field extensions based on the cyclotomic polynomials |
| title_sort |
normal high order elements in finite field extensions based on the cyclotomic polynomials |
| description |
We consider elements which are both of high multiplicative order and normal in extensions \(F_{q^{m} } \) of the field \(F_{q} \). If the extension is defined by a cyclotomic polynomial, we construct such elements explicitly and give explicit lower bounds on their orders. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2020 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1117 |
| work_keys_str_mv |
AT popovychr normalhighorderelementsinfinitefieldextensionsbasedonthecyclotomicpolynomials AT skuratovskiir normalhighorderelementsinfinitefieldextensionsbasedonthecyclotomicpolynomials |
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2025-12-02T15:41:53Z |
| last_indexed |
2025-12-02T15:41:53Z |
| _version_ |
1850411700242612224 |