The polynomial degree of the Grassmannian G1,n,2

Shaw, R.; Gordon, N. A.

Abstract

For a subset ψ of PG(N, 2) a known result states that ψ has polynomial degree ≤ r, r ≤ N, if and only if ψ intersects every r-flat of PG(N, 2) in an odd number of points. Certain refinements of this result are considered, and are then applied in the case when ψ is the Grassmannian G 1,n,2 ⊂ PG(N, 2), N = (n + 1/2} - 1, to show that for n < 8 the polynomial degree of G 1,n,2 is (n/2) - 1. © 2006 Springer Science+Business Media, Inc.

Citation

Shaw, R., & Gordon, N. A. (2006). The polynomial degree of the Grassmannian G1,n,2. Designs, codes, and cryptography, 39(2), 289-306. https://doi.org/10.1007/s10623-005-4524-4

• Journal Article Type: Article
• Acceptance Date: Aug 22, 2005
• Publication Date: 2006-05
• Journal: DESIGNS CODES AND CRYPTOGRAPHY
• Print ISSN: 0925-1022
• Electronic ISSN: 1573-7586
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 39
• Issue: 2
• Pages: 289-306
• DOI: https://doi.org/10.1007/s10623-005-4524-4
• Keywords: Applied Mathematics; Computer Science Applications
• Public URL: https://hull-repository.worktribe.com/output/396107
• Publisher URL: https://link.springer.com/article/10.1007%2Fs10623-005-4524-4