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

Authors

ZÜLFÜKAR SAYGI
ERNİST TİLENBAEV
ÇETİN ÜRTİŞ

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.

DOI

10.3906/mat-1805-113

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