Constructing irreducible polynomials with prescribed level curves over finite fields

Constructing irreducible polynomials with prescribed level curves over finite fields

We use Eisenstein's irreducibility criterion to prove that there exists an absolutely irreducible polynomial P(X,Y)∈GF(q)[X,Y] with coefficients in the finite field GF(q) with q elements, with prescribed level curves Xc:={(x,y)∈GF(q)2|P(x,y)=c}.

Bibliographic Details
Main Author: Mihai Caragiu
Format: Article
Language:English
Published: Hindawi Limited 2001-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/S0161171201011309
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spelling doaj-4833210dc6c14db5bf0800db81fbc3fc2020-11-24T22:54:34ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-0127419720010.1155/S0161171201011309Constructing irreducible polynomials with prescribed level curves over finite fieldsMihai Caragiu0The Institute of Mathematics at Bucharest, P.O. Box 1-764, RO-70700, RomaniaWe use Eisenstein's irreducibility criterion to prove that there exists an absolutely irreducible polynomial P(X,Y)∈GF(q)[X,Y] with coefficients in the finite field GF(q) with q elements, with prescribed level curves Xc:={(x,y)∈GF(q)2|P(x,y)=c}.http://dx.doi.org/10.1155/S0161171201011309
collection DOAJ
language English
format Article
sources DOAJ
author Mihai Caragiu
spellingShingle Mihai Caragiu
Constructing irreducible polynomials with prescribed level curves over finite fields
International Journal of Mathematics and Mathematical Sciences
author_facet Mihai Caragiu
author_sort Mihai Caragiu
title Constructing irreducible polynomials with prescribed level curves over finite fields
title_short Constructing irreducible polynomials with prescribed level curves over finite fields
title_full Constructing irreducible polynomials with prescribed level curves over finite fields
title_fullStr Constructing irreducible polynomials with prescribed level curves over finite fields
title_full_unstemmed Constructing irreducible polynomials with prescribed level curves over finite fields
title_sort constructing irreducible polynomials with prescribed level curves over finite fields
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2001-01-01
description We use Eisenstein's irreducibility criterion to prove that there exists an absolutely irreducible polynomial P(X,Y)∈GF(q)[X,Y] with coefficients in the finite field GF(q) with q elements, with prescribed level curves Xc:={(x,y)∈GF(q)2|P(x,y)=c}.
url http://dx.doi.org/10.1155/S0161171201011309
work_keys_str_mv AT mihaicaragiu constructingirreduciblepolynomialswithprescribedlevelcurvesoverfinitefields
_version_ 1725659109282283520

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