Fast construction of irreducible polynomials over finite fields
| hal.structure.identifier | Institut de Mathématiques de Toulouse UMR5219 [IMT] | |
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| hal.structure.identifier | Laboratoire International de Recherche en Informatique et Mathématiques Appliquées [LIRIMA] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | COUVEIGNES, Jean-Marc | |
| hal.structure.identifier | Institut de Recherche Mathématique de Rennes [IRMAR] | |
| dc.contributor.author | LERCIER, Reynald | |
| dc.date.accessioned | 2024-04-04T03:17:19Z | |
| dc.date.available | 2024-04-04T03:17:19Z | |
| dc.date.created | 2009-09-11 | |
| dc.date.issued | 2013 | |
| dc.identifier.issn | 0021-2172 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/194296 | |
| dc.description.abstractEn | We present a randomized algorithm that on input a finite field $K$ with $q$ elements and a positive integer $d$ outputs a degree $d$ irreducible polynomial in $K[x]$. The running time is $d^{1+o(1)} \times (\log q)^{5+o(1)}$ elementary operations. The $o(1)$ in $d^{1+o(1)}$ is a function of $d$ that tends to zero when $d$ tends to infinity. And the $o(1)$ in $(\log q)^{5+o(1)}$ is a function of $q$ that tends to zero when $q$ tends to infinity. In particular, the complexity is quasi-linear in the degree $d$. | |
| dc.language.iso | en | |
| dc.publisher | Springer | |
| dc.subject.en | number theory | |
| dc.subject.en | algebraic geometry | |
| dc.title.en | Fast construction of irreducible polynomials over finite fields | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1007/s11856-012-0070-8 | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.subject.hal | Mathématiques [math]/Géométrie algébrique [math.AG] | |
| dc.identifier.arxiv | 0905.1642 | |
| bordeaux.journal | Israel Journal of Mathematics | |
| bordeaux.page | 77-105 | |
| bordeaux.volume | 194 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 1 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00456456 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00456456v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Israel%20Journal%20of%20Mathematics&rft.date=2013&rft.volume=194&rft.issue=1&rft.spage=77-105&rft.epage=77-105&rft.eissn=0021-2172&rft.issn=0021-2172&rft.au=COUVEIGNES,%20Jean-Marc&LERCIER,%20Reynald&rft.genre=article |
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