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.
Keywords: Finite fields, normal bases, normal elements, $k$-normal elements
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