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A new construction procedure for caps of PG(3,q), q even. (Italian. English summary) Zbl 0552.51011

Suppose that N is a complete n-arc of \(PG(2,2^ h)\) such that there exists an irreducible conic C satisfying (i) If \(M=N\cap C,\) then \(| M| =n-3;\) (ii) the nucleus O of C belongs to N and the line joining the last two points \(Y_ 1\) and \(Y_ 2\) of N not lying on C is a secant of C; (iii) if \(P\not\in C\) and \(M\cup \{P\}\) is an arc, then either P is collinear with \(Y_ 1\) and \(Y_ 2\), or P coincides with O. Under such conditions the author constructs a complete k-cap with \(k=(n-3)(q+1)+2\) of \(PG(3,2^ h)\). He further gives an example with \(n=(q+8)/3,\) hence \(k=(q^ 2+5)/3,\) for any \(q=2^{2h},\) \(h\geq 4.\)
Reviewer: J.A.Thas

MSC:

51E20 Combinatorial structures in finite projective spaces
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