Normal high order elements in finite field extensions based on the cyclotomic polynomials
Roman Popovych, Ruslan Skuratovskii · Algebra and Discrete Mathematics · 2020
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.