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.File in questo prodotto:
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