A characterization of the primals in PG(m, 2)
Designs, Codes and Cryptography
Configurations of planes in PG(5,2)
Discrete Mathematics
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
Designs, Codes and Cryptography
The ψ-associate X# of a flat X in PG(n, 2)
Designs, Codes and Cryptography
On invariant notions of Segre varieties in binary projective spaces
Designs, Codes and Cryptography
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The Segre variety $${\mathcal{S}_{1,2}}$$ in PG(5, 2) is a 21-set of points which is shown to have a cubic equation Q(x) = 0. If T(x, y, z) denotes the alternating trilinear form obtained by completely polarizing the cubic polynomial Q, then the associate U # of an r-flat $${U \subset {\rm PG}(5, 2)}$$ is defined to be $$U^{\#} = \{z \in {\rm PG}(5, 2)\,|\,T(u_{1}, u_{2}, z) = 0\, {\rm for \, all}\, u_{1}, u_{2} \in U\},$$ and so is an s-flat for some s. Those lines L of PG(5, 2) which are singular, satisfying that is L # = PG(5.2), are shown to form a complete spread of 21 lines. For each r-flat $${U \subset {\rm PG}(5, 2)}$$ its associate U # is determined. Examples are given of four kinds of planes P which are self-associate, P # = P, and three kinds of planes for which P, P #, P ## are disjoint planes such that P ### = P.