Selfdual skew cyclic codes
| 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 | |
| hal.structure.identifier | Chercheur indépendant | |
| dc.contributor.author | DRAIN, Fabrice | |
| dc.date.accessioned | 2024-04-04T02:33:54Z | |
| dc.date.available | 2024-04-04T02:33:54Z | |
| dc.date.created | 2023-06 | |
| dc.date.issued | 2023-06-13 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190517 | |
| dc.description.abstractEn | Given a finite extension $\mathbf{K/F}$ of degree $r$ of a finite field $\mathbf{F}$ in characteristic $p$, we enumerate all selfdual skew cyclic codes in the Ore quotient ring $\mathbf{E}_{k}:=\mathbf{K}[X^{\pm 1};\Frob]/(X^{kr}-1)$ for any positive integer ${k}$ coprime to the characteristic $p$.We use a new approach based on vector space duality, which establishes an order reversing and orthogonality preserving bijection between skew codes and vector subspaces. Finally we implement this enumeration in SageMath. | |
| dc.description.sponsorship | Algèbre, preuves, protocoles, algorithmes, courbes, et surfaces pour les codes et leurs applications - ANR-21-CE39-0009 | |
| dc.language.iso | en | |
| dc.title.en | Selfdual skew cyclic codes | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math] | |
| 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-04127001 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-04127001v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2023-06-13&rft.au=CARUSO,%20Xavier&DRAIN,%20Fabrice&rft.genre=preprint |
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