Weighted intriguing sets of finite generalised quadrangles
A set of points \(\mathcal T\) of a generalised quadrangle of order \((s,t)\) is an \(i\)-tight set if for every point \(p\in {\mathcal T}\), there are \(s+i\) points of \(\mathcal T\) collinear with \(p\) and for every point \(p\notin {\mathcal T}\), there are \(i\) points of \(\mathcal T\) collinear with \(p\). A set of points \(\mathcal M\) of a generalised quadrangle is an \(m\)-ovoid if every line meets \({\mathcal M}\) in \(m\) points. Lemma 4.1. Let \(S\) be a set of points of a generalised quadrangle such that \(\chi_S\in (V^\epsilon)^\bot\) where \(\epsilon\in \{-,+\}\). Then \(S\) is an \(m\)-ovoid or a tight set. Theorem 9.1 Let \(S\) be a non-trivial \(m\)-ovoid of \(H(4,q^2)\). If \(q>2\), then \[ m\geq \frac{1}{2}\frac{-3q-3+\sqrt{4q^5-4q^4+5q^2-2q+1}}{q^2-q-2} \] where for \(q=2\) we have \(m\geq 2\).
scientific article; zbMATH DE number 6062482
scientific article