The geometric dimension of some small configurations
Document Type
Article
Publication Date
11-18-2012
Department
Department of Mathematical Sciences
Abstract
Recently, Jungnickel and Tonchev (Des Codes Cryptogr, doi:10.1007/s10623-012-9636-z, 2012) introduced new invariants for simple incidence structures D, which admit both a coding theoretic and a geometric description. Geometrically, one considers embeddings of D into projective geometries Π = PG(n, q), where an embedding means identifying the points of D with a point set V in Π in such a way that every block of D is induced as the intersection of V with a suitable subspace of Π. Then the new invariant, the geometric dimension geomdimq D of D, is the smallest value of n for which D may be embedded into the n-dimensional projective geometry PG(n, q). It is the aim of this paper to discuss a few additional general results regarding these invariants, and to determine them for some further examples, mainly some small configurations; this will answer some problems posed in (Des Codes Cryptogr, doi:10.1007/s10623-012-9636-z, 2012).
Publication Title
Journal of Geometry
Recommended Citation
DeWinter, S.,
&
Jungnickel, D.
(2012).
The geometric dimension of some small configurations.
Journal of Geometry,
103(3), 417-430.
http://doi.org/10.1007/s00022-012-0140-4
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/4629