Non-classical hyperplanes of \(\mathrm{DW}(5,q)\) (Q1953491)

Summary: The hyperplanes of the symplectic dual polar space \(\mathrm{DW}(5,q)\) arising from embedding, the so-called classical hyperplanes of \(\mathrm{DW}(5,q)\), have been determined earlier in the literature. In the present paper, we classify non-classical hyperplanes of \(\mathrm{DW}(5,q)\). If \(q\) is even, then we prove that every such hyperplane is the extension of a non-classical ovoid of a quad of \(\mathrm{DW}(5,q)\). If \(q\) is odd, then we prove that every non-classical ovoid of \(\mathrm{DW}(5,q)\) is either a semi-singular hyperplane or the extension of a non-classical ovoid of a quad of \(\mathrm{DW}(5,q)\). If \(\mathrm{DW}(5,q), q\) odd, has a semi-singular hyperplane, then \(q\) is not a prime number.