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.

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
• APA6 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