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

Authors : Zülfükar SAYGI, Ernist TİLENBAEV, Çetin ÜRTİŞ

Pages : 795-812

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Publication Date : 0000-00-00

Article Type : Research Paper

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. insert ignore into journalissuearticles values(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