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

Autor:	Ernist Tilenbaev, Zülfükar Saygı, Çetin Ürtiş
Přispěvatelé:	TOBB ETU, Faculty of Science and Literature, Depertment of Mathematics, TOBB ETÜ, Fen Edebiyat Fakültesi, Matematik Bölümü, Saygı, Zülfükar, Ürtiş, Çetin
Rok vydání:	2019
Předmět:	kk-normal elements Finite field General Mathematics Mathematical analysis normal elements Finite fields normal bases normal elements $k$-normal elements Finite fields normal bases Mathematics
Zdroj:	Volume: 43, Issue: 2 795-812 Turkish Journal of Mathematics
ISSN:	1300-0098 1303-6149
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::86e9d2557af42537f0fe7294f014c652 https://dergipark.org.tr/tr/pub/tbtkmath/issue/45654/575303 Zobrazit plný text záznamu