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Simultaneous Rational Function Reconstruction with Errors: Handling Multiplicities and Poles

Eleonora Guerrini 1 Kamel Lairedj 2 Romain Lebreton 1 Ilaria Zappatore 3 
1 ECO - Exact Computing
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
3 GRACE - Geometry, arithmetic, algorithms, codes and encryption
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
Abstract : In this paper we focus on extensions of evaluation interpolation methods for recovering rational functions, in the context of erroneous evaluations. This problem can be viewed both from a computer algebra and a coding theory point of view. In computer algebra, this is a generalization of Simultaneous Rational Function Reconstruction with errors, with multiprecision evaluation. From an error correcting codes point of view, this problem is related to the decoding of some algebraic codes such as Reed Solomon or Derivatives codes. We give conditions on the inputs of the problem which guarantee the uniqueness of the interpolant. Since we deal with rational functions, some evaluation points may be poles: a first contribution of this work is to correct any error in a scenario with poles and multiplicities that extends [KPY20]. Our second contribution is to adapt rational function reconstruction for random errors, and provide better conditions for uniqueness using interleaving techniques as in [GLZ21].
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03620179
Contributor : Ilaria Zappatore Connect in order to contact the contributor
Submitted on : Friday, March 25, 2022 - 3:52:57 PM
Last modification on : Tuesday, October 25, 2022 - 4:23:18 PM
Long-term archiving on: : Sunday, June 26, 2022 - 7:04:00 PM

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  • HAL Id : hal-03620179, version 1

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Eleonora Guerrini, Kamel Lairedj, Romain Lebreton, Ilaria Zappatore. Simultaneous Rational Function Reconstruction with Errors: Handling Multiplicities and Poles. {date}. ⟨hal-03620179⟩

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