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Simultaneous Rational Function Reconstruction with Errors: Handling Multiplicities and Poles
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].
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 : Friday, April 8, 2022 - 3:23:30 AM
Contributor : Ilaria Zappatore Connect in order to contact the contributor
Submitted on : Friday, March 25, 2022 - 3:52:57 PM
Last modification on : Friday, April 8, 2022 - 3:23:30 AM
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