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Ovals in \({\mathbb{Z}}^2_{2p} \). (English) Zbl 1453.51002
As a generalization of the classical definition for finite geometries, an oval in \(Z_{2p}^2\), where \(p\) is prime is defined as a set of \(2p+2\) points with the property that no three of them are on a line, where a line is the set of \((x,y)\) satisfying \(ax+by+c =0\) for some \(a, b, c\), where \(a, b\) and \(2p\) are relatively prime. The author proves that these ovals only exist when \(p=3\) or \(5\) and that they are unique up to isomorphism.
MSC:
51E21 Blocking sets, ovals, \(k\)-arcs
Keywords:
arc; collinearity; ovals
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