Perp-systems and partial geometries. (English) Zbl 0988.51006
Summary: A perp-system \(\mathcal R(r)\) is a maximal set of \(r\)-dimensional subspaces of \(PG(N,q)\) equipped with a polarity \(\rho\), such that the tangent space of an element of \(\mathcal R(r)\) does not intersect any element of \(\mathcal R(r)\).
We prove that a perp-system yields partial geometries, strongly regular graphs, two-weight codes, maximal arcs and \(k\)-ovoids. We also give some examples, one of them yielding a new \(pg(8,20,2)\).
We prove that a perp-system yields partial geometries, strongly regular graphs, two-weight codes, maximal arcs and \(k\)-ovoids. We also give some examples, one of them yielding a new \(pg(8,20,2)\).
MSC:
| 51E14 | Finite partial geometries (general), nets, partial spreads |
Keywords:
perp-system; partial geometries; strongly regular graphs; codes; maximal arcs; \(k\)-ovoidsReferences:
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