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Journal Articles Applicable Algebra in Engineering, Communication and Computing Year : 2013

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

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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Dates and versions

hal-00642075 , version 1 (17-11-2011)
hal-00642075 , version 2 (20-12-2013)

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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, 2013, 24 (6), pp.413-443. ⟨10.1007/s00200-013-0200-5⟩. ⟨hal-00642075v2⟩
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