Decomposable Subspaces, Linear Sections of Grassmann Varieties, and Higher Weights of Grassmann Codes

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dc.creatorGhorpade, Sudhir R.
dc.creatorPatil, Arunkumar R.
dc.creatorPillai, Harish K.
dc.date2007-10-26
dc.date.accessioned2026-07-07T12:57:54Z
dc.date.available2026-07-07T12:57:54Z
dc.descriptionGiven a homogeneous component of an exterior algebra, we characterize those subspaces in which every nonzero element is decomposable. In geometric terms, this corresponds to characterizing the projective linear subvarieties of the Grassmann variety with its Plucker embedding. When the base field is finite, we consider the more general question of determining the maximum number of points on sections of Grassmannians by linear subvarieties of a fixed (co)dimension. This corresponds to a known open problem of determining the complete weight hierarchy of linear error correcting codes associated to Grassmann varieties. We recover most of the known results as well as prove some new results. In the process we obtain, and utilize, a simple generalization of the Griesmer-Wei bound for arbitrary linear codes.
dc.description16 pages
dc.identifierhttps://arxiv.org/abs/0710.5161
dc.identifierhttp://arxiv.org/abs/0710.5161
dc.identifierFinite Fields Appl. 15 (2009), no. 1, 54--68.
dc.identifierdoi:10.1016/j.ffa.2008.08.001
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/225068
dc.subjectAlgebraic Geometry
dc.subjectInformation Theory
dc.subject15A75; 14M15; 94B05; 94B27
dc.titleDecomposable Subspaces, Linear Sections of Grassmann Varieties, and Higher Weights of Grassmann Codes
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