On the number of $k$-normal elements over finite fields

Authors

ZÜLFÜKAR SAYGI
ERNİST TİLENBAEV
ÇETİN ÜRTİŞ

DOI

10.3906/mat-1805-113

Abstract

In this article we give an explicit formula for the number of $k$-normal elements, hence answering Problem 6.1. of Huczynska et al. (Existence and properties of $k$-normal elements over finite fields, Finite Fields Appl 2013; 24: 170-183). Furthermore, for some cases we provide formulas that require the solutions of some linear Diophantine equations. Our results depend on the explicit factorization of cyclotomic polynomials.

Keywords

Finite fields, normal bases, normal elements, $k$-normal elements

First Page

795

Last Page

812

Recommended Citation

SAYGI, ZÜLFÜKAR; TİLENBAEV, ERNİST; and ÜRTİŞ, ÇETİN (2019) "On the number of $k$-normal elements over finite fields," Turkish Journal of Mathematics: Vol. 43: No. 2, Article 17. https://doi.org/10.3906/mat-1805-113
Available at: https://journals.tubitak.gov.tr/math/vol43/iss2/17