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}.
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| Format: | Article |
| Language: | English |
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Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201011309 |
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| _version_ | 1832567510519513088 |
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| author | Mihai Caragiu |
| author_facet | Mihai Caragiu |
| author_sort | Mihai Caragiu |
| collection | DOAJ |
| 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}. |
| format | Article |
| id | doaj-art-4833210dc6c14db5bf0800db81fbc3fc |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-4833210dc6c14db5bf0800db81fbc3fc2025-02-03T01:01:14ZengWileyInternational 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 |
| spellingShingle | Mihai Caragiu Constructing irreducible polynomials with prescribed level curves over finite fields International Journal of Mathematics and Mathematical Sciences |
| title | 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_short | Constructing irreducible polynomials with prescribed level curves over finite fields |
| title_sort | constructing irreducible polynomials with prescribed level curves over finite fields |
| url | http://dx.doi.org/10.1155/S0161171201011309 |
| work_keys_str_mv | AT mihaicaragiu constructingirreduciblepolynomialswithprescribedlevelcurvesoverfinitefields |