Turkish Journal of Mathematics
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, Z, TİLENBAEV, E, & ÜRTİŞ, Ç (2019). On the number of $k$-normal elements over finite fields. Turkish Journal of Mathematics 43 (2): 795-812. https://doi.org/10.3906/mat-1805-113
