The classification of flats in PG (9, 2) which are external to the grassmannian script G sign1,4,2

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

doi:10.1007/s10623-004-4855-6

Authors

Ron Shaw

Johannes G. Maks

Dr Neil Gordon N.A.Gordon@hull.ac.uk
Senior Lecturer

Abstract

Constructions are given of different kinds of flats in the projective space$$PG(9,2)={\mathbb P}(\wedge^{2}V(5,2))$$which are external to the Grassmannian$${\cal G}_{\bf 1,4,2}$$of lines ofPG(4,2). In particular it is shown that there exist precisely twoGL(5,2)-orbits of external 4-flats, each with stabilizer group &cong;31:5. (No 5-flat is external.) For eachk=1,2,3, two distinct kinds of externalk-flats are simply constructed out of certain partial spreads inPG(4,2) of sizek+2. A third kind of external plane, with stabilizer &cong;23:(7:3), is also shown to exist. With the aid of a certain `key counting lemma', it is proved that the foregoing amounts to a complete classification of external flats.

Journal Article Type	Article
Publication Date	2005-02
Journal	Designs, Codes, and Cryptography
Print ISSN	0925-1022
Electronic ISSN	1573-7586
Publisher	Springer Verlag
Peer Reviewed	Peer Reviewed
Volume	34
Issue	2-3
Pages	203-227
Institution Citation	Shaw, R., Maks, J. G., & Gordon, N. A. (2005). The classification of flats in PG (9, 2) which are external to the grassmannian script G sign1,4,2. Designs, codes, and cryptography, 34(2-3), 203-227. https://doi.org/10.1007/s10623-004-4855-6
DOI	https://doi.org/10.1007/s10623-004-4855-6
Keywords	Applied Mathematics; Computer Science Applications
Publisher URL	https://link.springer.com/article/10.1007%2Fs10623-004-4855-6