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Algebraic Geometry codes in the sum-rank metric
| hal.structure.identifier | Eindhoven University of Technology [Eindhoven] [TU/e] | |
| dc.contributor.author | BERARDINI, Elena | |
| hal.structure.identifier | Université de Bordeaux [UB] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| hal.structure.identifier | Analyse cryptographique et arithmétique [CANARI] | |
| dc.contributor.author | CARUSO, Xavier | |
| dc.date.accessioned | 2024-04-04T02:35:04Z | |
| dc.date.available | 2024-04-04T02:35:04Z | |
| dc.date.issued | 2023-03-15 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190602 | |
| dc.description.abstractEn | We introduce the first geometric construction of codes in the sum-rank metric, which we called linearized Algebraic Geometry codes, using quotients of the ring of Ore polynomials with coefficients in the function field of an algebraic curve. We study the parameters of these codes and give lower bounds for their dimension and minimum distance. Our codes exhibit quite good parameters, respecting a similar bound to Goppa's bound for Algebraic Geometry codes in the Hamming metric. | |
| dc.description.sponsorship | Algèbre, preuves, protocoles, algorithmes, courbes, et surfaces pour les codes et leurs applications - ANR-21-CE39-0009 | |
| dc.description.sponsorship | Correspondance de Langlands p-adique : une approche constructive et algorithmique - ANR-18-CE40-0026 | |
| dc.language.iso | en | |
| dc.subject.en | sum-rank metric codes | |
| dc.subject.en | algebraic curves | |
| dc.subject.en | function fields | |
| dc.subject.en | Ore polynomials | |
| dc.subject.en | finite fields | |
| dc.title.en | Algebraic Geometry codes in the sum-rank metric | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math] | |
| dc.identifier.arxiv | 2303.08903 | |
| dc.description.sponsorshipEurope | Marie Skłodowska–Curie grant agreement No 899987 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-04034810 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-04034810v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2023-03-15&rft.au=BERARDINI,%20Elena&CARUSO,%20Xavier&rft.genre=preprint |
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