Normal high order elements in finite field extensions based on the cyclotomic polynomials - Popovych, R.; Skuratovskii, R. (Algebra and Discrete Mathematics, 2020)
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.