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

Jérémy Berthomieu 1 Grégoire Lecerf 2 Guillaume Quintin 3, 2 
1 PolSys - Polynomial Systems
LIP6 - Laboratoire d'Informatique de Paris 6, Inria Paris-Rocquencourt
3 GRACE - Geometry, arithmetic, algorithms, codes and encryption
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
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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https://hal.inria.fr/hal-00642075
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Submitted on : Friday, December 20, 2013 - 5:27:58 PM
Last modification on : Friday, January 21, 2022 - 3:21:48 AM
Long-term archiving on: : Friday, March 21, 2014 - 9:26:04 AM

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Jérémy Berthomieu, Grégoire Lecerf, Guillaume Quintin. Polynomial root finding over local rings and application to error correcting codes. Applicable Algebra in Engineering, Communication and Computing, Springer Verlag, 2013, 24 (6), pp.413-443. ⟨10.1007/s00200-013-0200-5⟩. ⟨hal-00642075v2⟩

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