In this paper we prove the existence of a complete cap of PG(4n+1,q) of size 2(q(2n+1)-1)/(q-1), for each prime power q>2. It is obtained by projecting two disjoint Veronese varieties of PG(2n(2)+3n,q) from a suitable (2n(2)-n-2)-dimensional projective space. This shows that the trivial lower bound for the size of the smallest complete cap of PG(4n+1,q) is essentially sharp.

Small complete caps in PG(4n + 1, q)

Cossidente A.
Membro del Collaboration Group
;
Csajbok B.
Membro del Collaboration Group
;
Marino G.
Membro del Collaboration Group
;
Pavese F.
Membro del Collaboration Group
2023-01-01

Abstract

In this paper we prove the existence of a complete cap of PG(4n+1,q) of size 2(q(2n+1)-1)/(q-1), for each prime power q>2. It is obtained by projecting two disjoint Veronese varieties of PG(2n(2)+3n,q) from a suitable (2n(2)-n-2)-dimensional projective space. This shows that the trivial lower bound for the size of the smallest complete cap of PG(4n+1,q) is essentially sharp.
2023
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11563/173875
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