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Polynomial root finding over local rings and application to error correcting codes

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Abstract

This article is devoted to algorithms for computing all the roots of a univariate polynomial with coefficients in a complete commutative Noetherian unramified regular local domain, which are given to a fixed common finite precision. We study the cost of our algorithms, discuss their practical performances, and apply our results to the Guruswami and Sudan list decoding algorithm over Galois rings.

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Acknowledgments

This work has been partly supported by the French ANR-09-JCJC-0098-01 MaGiX project, and by the Digiteo 2009-36HD grant of the Région Île-de-France. We would like to thank Daniel Augot and both referees for their useful comments on this article.

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Authors and Affiliations

  1. UPMC, Univ. Paris 6, LIP6-INRIA Paris–Rocquencourt, POLSYS-CNRS UMR 7606, LIP6, Boîte courrier 169, 4 place Jussieu, 75252, Paris Cedex 5, France

    Jérémy Berthomieu

  2. Laboratoire d’Informatique, CNRS UMR 7161, LIX, Campus de l’École polytechnique, 91128, Palaiseau Cedex, France

    Grégoire Lecerf & Guillaume Quintin

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  1. Jérémy Berthomieu
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  2. Grégoire Lecerf
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  3. Guillaume Quintin
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Correspondence to Guillaume Quintin.

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Berthomieu, J., Lecerf, G. & Quintin, G. Polynomial root finding over local rings and application to error correcting codes. AAECC 24, 413–443 (2013). https://doi.org/10.1007/s00200-013-0200-5

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  • DOI: https://doi.org/10.1007/s00200-013-0200-5

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