Let ∆ be one of the dual polar spaces DQ(8, q), DQ−(7, q), and let e : ∆ → Σ denote the spin-embedding of ∆. We show that e(∆) is a two-intersection set of the projective space Σ. Moreover, if ∆ ∼= DQ−(7, q), then e(∆) is a (q + 1)-tight set of a nonsingular hyperbolic quadric Q(7, q) of Σ ∼= PG(7, q). This (q + 1)-tight set gives rise to more examples of… (More)
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