Rank-Metric Lattices

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dc.contributor.authorCotardo, Giuseppeen
dc.contributor.authorRavagnani, Albertoen
dc.date.accessioned2023-03-29T13:25:24Zen
dc.date.available2023-03-29T13:25:24Zen
dc.date.issued2023-01-13en
dc.description.abstractWe introduce the class of rank-metric geometric lattices and initiate the study of their structural properties. Rank-metric lattices can be seen as the q-analogues of higher-weight Dowling lattices, defined by Dowling himself in 1971. We fully characterize the supersolvable rank-metric lattices and compute their characteristic polynomials. We then concentrate on small rank-metric lattices whose characteristic polynomial we cannot compute, and provide a formula for them under a polyno-miality assumption on their Whitney numbers of the first kind. The proof relies on computational results and on the theory of vector rank-metric codes, which we review in this paper from the perspective of rank-metric lattices. More precisely, we introduce the notion of lattice-rank weights of a rank-metric code and inves-tigate their properties as combinatorial invariants and as code distinguishers for inequivalent codes.Mathematics Subject Classifications: 05A15, 06C10, 94B99en
dc.description.notesSupported by the Irish Research Council, grant n. GOIPG/2018/2534. Supported by the Dutch Research Council through grants VI.Vidi.203.045, OCENW.KLEIN.539, and by the Royal Academy of Arts and Sciences of the Netherlands.en
dc.description.sponsorshipIrish Research Council [GOIPG/2018/2534]; Dutch Research Council [VI.Vidi.203.045, OCENW.KLEIN.539]; Royal Academy of Arts and Sciences of the Netherlandsen
dc.description.versionPublished versionen
dc.format.mimetypeapplication/pdfen
dc.identifier.doihttps://doi.org/10.37236/11373en
dc.identifier.issue1en
dc.identifier.urihttp://hdl.handle.net/10919/114221en
dc.identifier.volume30en
dc.language.isoenen
dc.publisherElectronic Journal Of Combinatoricsen
dc.rightsCreative Commons Attribution-NoDerivatives 4.0 Internationalen
dc.rights.urihttp://creativecommons.org/licenses/by-nd/4.0/en
dc.subjectWeighten
dc.subjectcodesen
dc.subjectgenericityen
dc.subjectgeometriesen
dc.titleRank-Metric Latticesen
dc.title.serialElectronic Journal of Combinatoricsen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten

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