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

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... Read More

Partial spreads in PG(4,2) and flats in PG(9,2) external to the Grassmannian G1,4,2 (2005)
Journal Article
Maks, J. G., Shaw, R., & Gordon, N. A. (2005). Partial spreads in PG(4,2) and flats in PG(9,2) external to the Grassmannian G1,4,2. Discrete Mathematics, 301(1), 137-146. doi:10.1016/j.disc.2004.11.023

We consider the following 'even hyperplane construction'of flats in the projective space PG(9, 2) = P(boolean AND(2) V(5, 2)) which are external to the Grassmannian G(1,4,2) of lines of PG(4,2). Let the Grassmann image in G(1,4,2) of a partial spread... Read More