We present a survey on classical problems of Galois geometries. More precisely we discuss some problems and results about ovals, hyperovals, caps, maximal arcs and blocking sets in projective planes and spaces over Galois fields.
We determine the minimum number of blocks in a partition of a finite pre-ordered set into chains, unrelated and ordered subsets respectively.
Ruled systems of the second kind (cf. [5], [6], [7]) are studied. It is proved that such a system, when satisfying suitable graphic and arithmetical conditions, is isomorphic to a non-singular quadric of S.
In this paper it is shown that a ruled system of the second kind (cf. [5], [10], [12]), satisfying suitable graphic and arithmetical conditions, is isomorphic to an elliptic quadric of (with odd q).
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