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 Fqm of the field Fq. 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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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2020 |
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| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/188518 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Normal high order elements in finite field extensions based on the cyclotomic polynomials / R. Popovych, R. Skuratovskii // Algebra and Discrete Mathematics. — 2020. — Vol. 29, № 2. — С. 241–248. — Бібліогр.: 9 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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Popovych, R. Skuratovskii, R. 2023-03-03T19:50:31Z 2023-03-03T19:50:31Z 2020 Normal high order elements in finite field extensions based on the cyclotomic polynomials / R. Popovych, R. Skuratovskii // Algebra and Discrete Mathematics. — 2020. — Vol. 29, № 2. — С. 241–248. — Бібліогр.: 9 назв. — англ. 1726-3255 DOI:10.12958/adm1117 2010 MSC: 11T30. https://nasplib.isofts.kiev.ua/handle/123456789/188518 We consider elements which are both of high multiplicative order and normal in extensions Fqm of the field Fq. If the extension is defined by a cyclotomic polynomial, we construct such elements explicitly and give explicit lower bounds on their orders. The authors are grateful to the referee for comments and suggestions which improved the quality of this paper. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Normal high order elements in finite field extensions based on the cyclotomic polynomials Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Normal high order elements in finite field extensions based on the cyclotomic polynomials |
| spellingShingle |
Normal high order elements in finite field extensions based on the cyclotomic polynomials Popovych, R. Skuratovskii, R. |
| 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 |
| author |
Popovych, R. Skuratovskii, R. |
| author_facet |
Popovych, R. Skuratovskii, R. |
| publishDate |
2020 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| description |
We consider elements which are both of high multiplicative order and normal in extensions Fqm of the field Fq. If the extension is defined by a cyclotomic polynomial, we construct such elements explicitly and give explicit lower bounds on their orders.
|
| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/188518 |
| citation_txt |
Normal high order elements in finite field extensions based on the cyclotomic polynomials / R. Popovych, R. Skuratovskii // Algebra and Discrete Mathematics. — 2020. — Vol. 29, № 2. — С. 241–248. — Бібліогр.: 9 назв. — англ. |
| work_keys_str_mv |
AT popovychr normalhighorderelementsinfinitefieldextensionsbasedonthecyclotomicpolynomials AT skuratovskiir normalhighorderelementsinfinitefieldextensionsbasedonthecyclotomicpolynomials |
| first_indexed |
2025-11-27T19:08:27Z |
| last_indexed |
2025-11-27T19:08:27Z |
| _version_ |
1850852678793428992 |