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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. https://doi.org/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 about The polynomial degree of the Grassmannian G1,n,2.

Partial spreads in PG(4,2) and flats in PG(9,2) external to the Grassmannian G1,4,2 (2005)
Journal Article
Shaw, R., Gordon, N. A., & Maks, J. G. (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. https://doi.org/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 about Partial spreads in PG(4,2) and flats in PG(9,2) external to the Grassmannian G1,4,2.

The quintic Grassmannian g(1,4,2) in PG(9,2) (2004)
Journal Article
Shaw, R., & Gordon, N. (2004). The quintic Grassmannian g(1,4,2) in PG(9,2). Designs, codes, and cryptography, 32(1-3), 381 - 396. https://doi.org/10.1023...ESI.0000029236.10701.61

The 155 points of the Grassmannian g(1,4,2) of lines of PG(4,2) = PV(5,2) are those points x is an element of PG(9,2) = P(boolean AND V-2(5,2)) which satisfy a certain quintic equation Q(x) = 0. (The quintic polynomial Q is given explicitly in Shaw a... Read More about The quintic Grassmannian g(1,4,2) in PG(9,2).


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