The second-order factorable core of polynomials over finite fields
type: Item
instance of: scholarly article
title: The second-order factorable core of polynomials over finite fields
zbMATH Open document ID: 0929.11058
author: Maria T. Acosta
author: Javier Gomez-Calderon
published in: Rocky Mountain Journal of Mathematics
publication date: 1999-10-17T00:00:00Z
full work available at URL: CONT29-1.html
review text: The authors look at polynomials \(f^*(x,y)= f(x)-f(y)\) where \(f(x)\in \mathbb{F}_q [x]\) over a finite field \(\mathbb{F}_q\). A sample result from the paper is given as follows. Let \(s\in\mathbb{N}\) be the number of quadratic irreducible factors of \(f^*(x,y)\) over the algebraic closure of \(\mathbb{F}_q\), having no \(xy\) term. Then, under a suitable hypothesis, \(f(x-c)=h ((x^2+b)^{s +1})\) for some \(h(x)\in \mathbb{F}_q[x]\), where \(f(x)= aD(x+b)+c\), and \(D(x)\) is a suitable chosen Dickson polynomial.
Mathematics Subject Classification ID: 11T06
Mathematics Subject Classification ID: 11C08
zbMATH DE Number: 1309606
zbMATH Keywords: quadratic factor
zbMATH Keywords: polynomials
zbMATH Keywords: finite field
zbMATH Keywords: Dickson polynomial
reviewed by: Richard A. Mollin
MaRDI profile type: Publication
OpenAlex ID: W1969598434
cites work: Q3351476
cites work: Exceptional polynomials and the reducibility of substitution polynomials
cites work: Polynomials with small value set over finite fields
cites work: A geometric approach to permutation polynomials over a finite field
cites work: Q3773972
DOI: 10.1216/RMJM/1181071676
description: scientific article; zbMATH DE number 1309606