Exponents of skew polynomials.
type: Item
instance of: scholarly article
title: Exponents of skew polynomials.
zbMATH Open document ID: 1343.16019
author: Ahmed Cherchem
author: André Leroy
published in: Finite Fields and their Applications
publication date: 2015-12-17T00:00:00Z
review text: Let \(f(x)\in\mathbb F_q[x]\) such that \(f(0)\neq 0\), where \(\mathbb F_q\) is a finite field. It is known that there exists a positive integer \(e=e(f)\) such that \(f(x)\) divides \(x^e-1\). The least such \(e\) is called the exponent of \(f(x)\). In this paper, the authors generalize this notion. Namely, they introduce and study the notion of exponent of a polynomial in an Ore extension \(\mathbb F_q[t;\theta]\), where \(\theta\) is the Frobenius automorphism of \(\mathbb F_q\).
Mathematics Subject Classification ID: 16S36
Mathematics Subject Classification ID: 11T55
Mathematics Subject Classification ID: 12Y05
Mathematics Subject Classification ID: 11T71
zbMATH DE Number: 6521809
zbMATH Keywords: polynomials over finite fields
zbMATH Keywords: skew polynomial rings
zbMATH Keywords: periods of polynomials
MaRDI profile type: Publication
full work available at URL: j.ffa.2015.08.004
OpenAlex ID: W1654919207
cites work: Coding with skew polynomial rings
cites work: Linear codes using skew polynomials with automorphisms and derivations
cites work: \((\sigma, \delta)\)-codes
cites work: Pseudo linear transformations and evaluation in Ore extensions
cites work: Noncommutative polynomial maps.
cites work: Q4301239
cites work: Convolutional codes with additional algebraic structure
DOI: 10.1016/J.FFA.2015.08.004
description: scientific article; zbMATH DE number 6521809