Primitive normal polynomials with the last half coefficients prescribed
type: Item
instance of: scholarly article
title: Primitive normal polynomials with the last half coefficients prescribed
zbMATH Open document ID: 1215.11115
author: Shuqin Fan
published in: Finite Fields and their Applications
publication date: 2011-02-14T00:00:00Z
review text: The author proves that for any given \(n\geq 2\) there exists a constant \(c(n)\) such that for any prime power \(q>c(n)\) there exists a primitive normal polynomial of degree \(n\) over \(\mathbb F_q\) with the last \(\lfloor n/2\rfloor\) coefficients prescribed and the last coefficient is a primitive element of \(\mathbb F_q\). If the prescribed coefficients are \((0,\dots,0,b)\) and \(n\) is odd, one more coefficient can be prescribed. This complements and partly improves the results of \textit{S. Q. Fan, W. B. Han} and \textit{K. Q. Feng} [``Primitive normal polynomials with multiple coefficients prescribed: an asymptotic result'', Finite Fields Appl. 13, No. 4, 1029--1044 (2007; Zbl 1132.11054)].
reviewed by: Arne Winterhof
Mathematics Subject Classification ID: 11T06
Mathematics Subject Classification ID: 11T24
zbMATH DE Number: 5851247
zbMATH Keywords: finite fields
zbMATH Keywords: primitive polynomials
zbMATH Keywords: character sums over Galois rings
zbMATH Keywords: Kloosterman sums
zbMATH Keywords: normal basis
zbMATH Keywords: \(p\)-adic method
zbMATH Keywords: prescribed coefficients
MaRDI profile type: Publication
full work available at URL: j.ffa.2009.05.004
OpenAlex ID: W1988003586
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cites work: Primitivity, freeness, norm and trace
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cites work: $p$ -ADIC FORMAL SERIES AND COHENS PROBLEM This work was supported by NSF of China with contract No. 19971096 and No. 90104035.
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DOI: 10.1016/J.FFA.2009.05.004
description: scientific article; zbMATH DE number 5851247