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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.

Authors

Ron Shaw

Johannes G. Maks

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 ≅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 ≅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