Geodesic
Normal high order elements in finite field extensions based on the cyclotomic polynomials
Algebra and discrete mathematics, Tome 29 (2020) no. 2, pp. 241-248

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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.
Keywords: finite field, normal basis, high multiplicative order element.
Mots-clés : cyclotomic polynomial 
@article{ADM_2020_29_2_a8,
     author = {R. Popovych and R. Skuratovskii},
     title = {Normal high order elements in finite field extensions based on the cyclotomic polynomials},
     journal = {Algebra and discrete mathematics},
     pages = {241--248},
     publisher = {mathdoc},
     volume = {29},
     number = {2},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2020_29_2_a8/}
}
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R. Popovych; R. Skuratovskii. Normal high order elements in finite field extensions based on the cyclotomic polynomials. Algebra and discrete mathematics, Tome 29 (2020) no. 2, pp. 241-248. http://geodesic.mathdoc.fr/item/ADM_2020_29_2_a8/