Elements of high order in finite fields specified by binomials

Keywords:
finite field, multiplicative order, element of high multiplicative order, binomial
Published online:
2022-06-30
Abstract
Let be a field with elements, where is a power of a prime number . For any integer and such that the polynomial is irreducible in , we combine two different methods to explicitly construct elements of high order in the field . Namely, we find elements with multiplicative order of at least , which is better than previously obtained bound for such family of extension fields.
How to Cite
(1)
Bovdi, V.; Diene, A.; Popovych, R. Elements of High Order in Finite Fields Specified by Binomials. Carpathian Math. Publ. 2022, 14, 238-246.