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Selfdual skew cyclic codes

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierLithe and fast algorithmic number theory [LFANT]
hal.structure.identifierAnalyse cryptographique et arithmétique [CANARI]
dc.contributor.authorCARUSO, Xavier
hal.structure.identifierChercheur indépendant
dc.contributor.authorDRAIN, Fabrice
dc.date.accessioned2024-04-04T02:33:54Z
dc.date.available2024-04-04T02:33:54Z
dc.date.created2023-06
dc.date.issued2023-06-13
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/190517
dc.description.abstractEnGiven 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.sponsorshipAlgèbre, preuves, protocoles, algorithmes, courbes, et surfaces pour les codes et leurs applications - ANR-21-CE39-0009
dc.language.isoen
dc.title.enSelfdual skew cyclic codes
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-04127001
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-04127001v1
bordeaux.COinSctx_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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