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The polynomial degree of the Grassmannian G1,n,2

Shaw, R.; Gordon, N. A.

Authors

R. Shaw



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.

Journal Article Type Article
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
APA6 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
DOI https://doi.org/10.1007/s10623-005-4524-4
Keywords Applied Mathematics; Computer Science Applications
Publisher URL https://link.springer.com/article/10.1007%2Fs10623-005-4524-4
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