On the generation of dual polar spaces of symplectic type over finite fields
Journal of Combinatorial Theory Series A
On the universal embedding of the Sp2n(2) dual polar space
Journal of Combinatorial Theory Series A
The universal embedding dimension of the binary symplectic dual polar space
Discrete Mathematics - The 2000 Com2MaC conference on association schemes, codes and designs
Valuations and hyperplanes of dual polar spaces
Journal of Combinatorial Theory Series A
Minimal full polarized embeddings of dual polar spaces
Journal of Algebraic Combinatorics: An International Journal
The hyperplanes of DQ(2n,K) and DQ-(2n+1,q) which arise from their spin-embeddings
Journal of Combinatorial Theory Series A
Note: A geometric description of the spin-embedding of symplectic dual polar spaces of rank 3
Journal of Combinatorial Theory Series A
On the nucleus of the Grassmann embedding of the symplectic dual polar space DSp(2n,F), char(F)=2
European Journal of Combinatorics
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Let ${\mathbb{K}}$ be a perfect field of characteristic 2. In this paper, we classify all hyperplanes of the symplectic dual polar space $DW(5,{\mathbb{K}})$ that arise from its Grassmann embedding. We show that the number of isomorphism classes of such hyperplanes is equal to 5+N, where N is the number of equivalence classes of the following equivalence relation R on the set $\{\lambda\in {\mathbb{K}}\,|\,X^{2}+\lambda X+1\mbox{ isirreducible}$ $\mbox{in }{\mathbb{K}}[X]\}$ : (驴 1,驴 2)驴R whenever there exists an automorphism 驴 of ${\mathbb{K}}$ and an $a\in {\mathbb{K}}$ such that (驴 2 驴 )驴1=驴 1 驴1 +a 2+a.