Partial spreads in PG(4,2) and flats in PG(9,2) external to the Grassmannian G1,4,2

Shaw, Ron; Gordon, Neil A.; Maks, Johannes G.

Abstract

We consider the following 'even hyperplane construction'of flats in the projective space PG(9, 2) = P(boolean AND(2) V(5, 2)) which are external to the Grassmannian G(1,4,2) of lines of PG(4,2). Let the Grassmann image in G(1,4,2) of a partial spread S-r = {mu(1),..., mu(r)} in PG(4,2) be C-r = {m(1,)..., m(r)}. Then C-r is an r-cap on G(1.4.2). Using the recent classification [N.A. Gordon, R. Shaw, L.H. Soicher, Classification of Partial Spreads in PG(4,2), pp. 63, available from: http://www.hull.ac.uk/maths/people/rs/staffdetails. html] of partial spreads in PG(4,2), we determine those partial spreads S-r such that the projective space E(C-r) = < C-r>,en generated by the ((r)(2)) points m(ij) := m(i) + m(j) is an external flat. We show 2 that, in this simple manner, we may construct seven out of the ten GL(5,2)-orbits of external flats. (c) 2005 Elsevier B.V. All rights reserved.

Citation

Shaw, R., Gordon, N. A., & Maks, J. G. (2005). Partial spreads in PG(4,2) and flats in PG(9,2) external to the Grassmannian G1,4,2. Discrete Mathematics, 301(1), 137-146. https://doi.org/10.1016/j.disc.2004.11.023

• Journal Article Type: Article
• Acceptance Date: Nov 8, 2004
• Online Publication Date: Aug 18, 2005
• Publication Date: 2005-09
• Journal: DISCRETE MATHEMATICS
• Print ISSN: 0012-365X
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 301
• Issue: 1
• Pages: 137-146
• DOI: https://doi.org/10.1016/j.disc.2004.11.023
• Keywords: Theoretical Computer Science; Discrete Mathematics and Combinatorics
• Public URL: https://hull-repository.worktribe.com/output/391619