A characterization of the primals in PG(m, 2)
Designs, Codes and Cryptography
The lines of PG(4, 2) are the points on a quintic in PG(9, 2)
Journal of Combinatorial Theory Series A
A property of A7, and a maximal 3-dimensional linear section of GL(4,2)
Discrete Mathematics
Configurations of planes in PG(5,2)
Discrete Mathematics
Designs, Codes and Cryptography
Subsets of PG(n,2) and Maximal Partial Spreads in PG(4,2)
Designs, Codes and Cryptography
The Quintic Grassmannian G1, 4, 2 in PG(9, 2)
Designs, Codes and Cryptography
The Polynomial Degree of the Grassmannian $${\mathcal G_{\bf 1,}{\bf n,}{\bf 2}}$$
Designs, Codes and Cryptography
The ψ-associate X# of a flat X in PG(n, 2)
Designs, Codes and Cryptography
The cubic Segre variety in PG(5, 2)
Designs, Codes and Cryptography
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Constructions are given of different kinds of flats in the projective space $$PG(9,2)={\mathbb P}(\wedge^{2}V(5,2))$$ which are external to the Grassmannian $${\cal G}_{\bf 1,4,2}$$ of lines of PG(4,2). In particular it is shown that there exist precisely two GL(5,2)-orbits of external 4-flats, each with stabilizer group 驴31:5. (No 5-flat is external.) For each k=1,2,3, two distinct kinds of external k-flats are simply constructed out of certain partial spreads in PG(4,2) of size k+2. A third kind of external plane, with stabilizer 驴23:(7:3), is also shown to exist. With the aid of a certain `key counting lemma驴, it is proved that the foregoing amounts to a complete classification of external flats.