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

  • Jérémy Berthomieu
  • Grégoire Lecerf
  • Guillaume Quintin
Original Paper

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.

Keywords

Polynomial root finding Galois ring List decoding  Guruswami–Sudan algorithm 

Mathematics Subject Classification (2000)

12Y05 94B05 

Notes

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jérémy Berthomieu
    • 1
  • Grégoire Lecerf
    • 2
  • Guillaume Quintin
    • 2
  1. 1.UPMC, Univ. Paris 6, LIP6-INRIA Paris–Rocquencourt, POLSYS-CNRS UMR 7606, LIP6Paris Cedex 5France
  2. 2.Laboratoire d’InformatiqueCNRS UMR 7161, LIXPalaiseau CedexFrance

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