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| HAL: hal-00456456, version 1 |
| arXiv: 0905.1642 |
| Detailed view |  Export this paper |
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| Israël Journal of Mathematics 194, 1 (2013) 77-105 |
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| Fast construction of irreducible polynomials over finite fields |
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| Jean-Marc Couveignes 1, 2Reynald Lercier 3 |
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| (2013) |
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| 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 $d$. |
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| 1: | Institut de Mathématiques de Toulouse (IMT) |
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Université Paul Sabatier [UPS] - Toulouse III – Université Toulouse le Mirail - Toulouse II – Université des Sciences Sociales - Toulouse I – Institut National des Sciences Appliquées (INSA) - Toulouse – CNRS : UMR5219 |
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| 2: | LFANT (INRIA Bordeaux - Sud-Ouest) |
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INRIA – Université de Bordeaux – CNRS : UMR5251 |
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| 3: | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| Géométrie algébrique réelle |
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| Subject | : | Mathematics/Number Theory Mathematics/Algebraic Geometry |
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| number theory – algebraic geometry |
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| Fulltext link: |
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| http://fr.arXiv.org/abs/0905.1642 |
| hal-00456456, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00456456 | |
| oai:hal.archives-ouvertes.fr:hal-00456456 | |
| From: Marie-Annick Guillemer | |
| Submitted on: Monday, 15 February 2010 11:05:47 | |
| Updated on: Thursday, 2 May 2013 09:28:13 | |
