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Duals of linearized Reed-Solomon codes

Xavier Caruso 1, 2 Amaury Durand 1, 2
2 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : We give a description of the duals of linearized Reed-Solomon codes in terms of codes obtained by taking residues of Ore rational functions. Our construction shows in particular that, under some assumptions on the base field, the class of linearized Reed-Solomon codes is stable under duality. As a byproduct of our work, we develop a theory of residues in the Ore setting.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03395402
Contributor : Xavier Caruso Connect in order to contact the contributor
Submitted on : Friday, October 22, 2021 - 1:56:11 PM
Last modification on : Wednesday, February 2, 2022 - 3:54:17 PM
Long-term archiving on: : Sunday, January 23, 2022 - 8:01:47 PM

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  • HAL Id : hal-03395402, version 1
  • ARXIV : 2110.12675

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Xavier Caruso, Amaury Durand. Duals of linearized Reed-Solomon codes. 2021. ⟨hal-03395402⟩

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