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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:
 5.1e+22 Blocking sets, ovals, $$k$$-arcs
##### Keywords:
arc; collinearity; ovals
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##### References:
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