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, extending the results of [7].
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Notes
For the left division, we use that \(\theta \) is bijective.
Note that, in the differential setting, the extension K/F is purely inseparable, so the usual trace map \(\mathrm{Tr}_{K/F}\) vanishes.
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Funding was provided by Agence Nationale de la Recherche Grant no. (ANR-18- CE40-0026-01 (CLap-CLap).
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Communicated by G. Korchmaros.
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Caruso, X., Durand, A. Duals of linearized Reed–Solomon codes. Des. Codes Cryptogr. 91, 241–271 (2023). https://doi.org/10.1007/s10623-022-01102-7
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DOI: https://doi.org/10.1007/s10623-022-01102-7