Codes from unit groups of division algebras over number fields
| hal.structure.identifier | Laboratoire de Mathématiques de Besançon (UMR 6623) [LMB] | |
| dc.contributor.author | MAIRE, Christian | |
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | PAGE, Aurel | |
| dc.date.accessioned | 2024-04-04T02:50:17Z | |
| dc.date.available | 2024-04-04T02:50:17Z | |
| dc.date.created | 2019 | |
| dc.date.issued | 2021 | |
| dc.identifier.issn | 0025-5874 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191898 | |
| dc.description.abstractEn | Lenstra and Guruswami described number field analogues of the algebraic geometry codes of Goppa. Recently, the first author and Oggier generalised these constructions to other arithmetic groups: unit groups in number fields and orders in division algebras; they suggested to use unit groups in quaternion algebras but could not completely analyse the resulting codes. We prove that the noncommutative unit group construction yields asymptotically good families of codes for the sum-rank metric from division algebras of any degree, and we estimate the size of the alphabet in terms of the degree. | |
| dc.description.sponsorship | Familles de fonctions L: analyse, interactions, résultats effectifs - ANR-17-CE40-0012 | |
| dc.description.sponsorship | Ingénierie et Innovation par les sciences physiques, les savoir-faire technologiques et l'interdisciplinarité - ANR-17-EURE-0002 | |
| dc.language.iso | en | |
| dc.publisher | Springer | |
| dc.subject.en | Division Algebras over Number Fields | |
| dc.subject.en | Asymptotically Good Codes | |
| dc.subject.en | Number Field Codes | |
| dc.subject.en | sum-rank metric | |
| dc.title.en | Codes from unit groups of division algebras over number fields | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1007/s00209-020-02614-5 | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.subject.hal | Mathématiques [math]/Théorie de l'information et codage [math.IT] | |
| dc.identifier.arxiv | 1804.07108 | |
| bordeaux.journal | Mathematische Zeitschrift | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01770396 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01770396v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Mathematische%20Zeitschrift&rft.date=2021&rft.eissn=0025-5874&rft.issn=0025-5874&rft.au=MAIRE,%20Christian&PAGE,%20Aurel&rft.genre=article |
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