The classification of flats in \(\text{PG}(\mathbf{9,2})\) which are external to the Grassmannian \({\mathcal G}_{\mathbf{1,4,2}}\)

DOI10.1007/s10623-004-4855-6zbMath1077.51001OpenAlexW2016091231MaRDI QIDQ1766107

Johannes G. Maks, Neil A. Gordon, Shaw, Ron

Publication date: 28 February 2005

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10623-004-4855-6

zbMATH Keywords

Grassmannianexternal flats\(\text{GL}(5,2)\)

Mathematics Subject Classification ID

Grassmannians, Schubert varieties, flag manifolds (14M15) Combinatorial structures in finite projective spaces (51E20)

Related Items (5)

The polynomial degrees of Grassmann and Segre varieties over GF(2) ⋮ The polynomial degree of the Grassmannian \({\mathcal G}_{1,n,2}\) ⋮ The cubic Segre variety in \(\mathrm{PG}(5,2)\) ⋮ The \(\psi\)-associate \(X^{\#}\) of a flat \(X\) in \(PG(n,2)\) ⋮ Partial spreads in PG(4,\,2) and flats in PG(9,\,2) external to the Grassmannian \(G_{1,4,2}\)

Cites Work

• A characterization of the primals in \(PG(m,2)\)
• The lines of \(PG(4, 2)\) are the points on a quintic in \(PG(9, 2)\)
• External flats to varieties in \(\mathbb{P}\mathbb{G}(\bigwedge^2(V))\) over finite fields
• Conclaves of planes in PG\((4,2)\) and certain planes external to the Grassmannian \(\mathcal G_{1,4,2} \subset \text{PG}(9,2)\)
• On tangent spaces and external flats to Grassmannians of lines over finite fields
• Configurations of planes in PG(5,2)
• Partial spreads in PG(4,\,2) and flats in PG(9,\,2) external to the Grassmannian \(G_{1,4,2}\)
• Optimal subcodes of second order Reed-Muller codes and maximal linear spaces of bivectors of maximal rank
• Subsets of PG\((n,2)\) and maximal partial spreads in PG\((4,2)\)

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