Normal high order elements in finite field extensions based on the cyclotomic polynomials

• Datum: 2020
• Hauptverfasser: Popovych, R., Skuratovskii, R.
• Format: Artikel
• Sprache: English
• Veröffentlicht: Lugansk National Taras Shevchenko University 2020
• Schlagworte: finite field; cyclotomic polynomial; normal basis; high multiplicative order element; 11T30
• Online Zugang: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1117
• Назва журналу: Algebra and Discrete Mathematics

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.