On \(\mathbb{F}_q\)-Order of Polynomials and Properties of \(r\)-Primitive and \(k\)-Normal Elements over Finite Fields

Fuente: arXiv
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Autori principali: K., Maithri, R., Vadiraja Bhatta G., P., Indira K., Poojary, Prasanna
Natura: Preprint
Pubblicazione: 2026
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author K., Maithri
R., Vadiraja Bhatta G.
P., Indira K.
Poojary, Prasanna
author_facet K., Maithri
R., Vadiraja Bhatta G.
P., Indira K.
Poojary, Prasanna
contents Polynomials and elements over finite fields exhibit closely related algebraic structures, and many properties defined for elements extend naturally to polynomials. The concepts of order and $\mathbb{F}_q$-Order for elements have been extensively studied. In this paper, we investigate several properties of $r$-primitive and $k$-normal elements. Furthermore, by using the concept of the $\mathbb{F}_q$-Order of a polynomial, we explore properties of $k$-normal polynomials.
format Preprint
id arxiv_https___arxiv_org_abs_2601_09201
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle On \(\mathbb{F}_q\)-Order of Polynomials and Properties of \(r\)-Primitive and \(k\)-Normal Elements over Finite Fields
K., Maithri
R., Vadiraja Bhatta G.
P., Indira K.
Poojary, Prasanna
Rings and Algebras
Polynomials and elements over finite fields exhibit closely related algebraic structures, and many properties defined for elements extend naturally to polynomials. The concepts of order and $\mathbb{F}_q$-Order for elements have been extensively studied. In this paper, we investigate several properties of $r$-primitive and $k$-normal elements. Furthermore, by using the concept of the $\mathbb{F}_q$-Order of a polynomial, we explore properties of $k$-normal polynomials.
title On \(\mathbb{F}_q\)-Order of Polynomials and Properties of \(r\)-Primitive and \(k\)-Normal Elements over Finite Fields
topic Rings and Algebras
url https://arxiv.org/abs/2601.09201