Regular Article
Small Complete Caps in Spaces of Even Characteristic

https://doi.org/10.1006/jcta.1996.0064Get rights and content
Under an Elsevier user license
open archive

Abstract

In 1959, Segre constructed a complete (3q+2)-cap inPG(3, q),qeven. This showed that the size of the smallest completek-cap inPG(3, q),qeven, is almost equal to the trivial lower bound which is of order[formula]. Generalizing the construction of Segre, complete (qn+3(qn−1+…+q)+2)-caps inPG(2nq),qeven,q⩾4, and complete (3(qn+…+q)+2)-caps inPG(2n+1, q),qeven,q⩾4, are constructed. This shows that in all spacesPG(2n+1, q),qeven, the size of the smallest completek-cap is almost equal to the trivial lower bound which is of order[formula].

Cited by (0)

This work is part of the national research projectStrutture Geometriche,Combinatoria e loro applicazioniof the ministry of university and scientific and technological research, at the mathematics department of Università degli Studi di Perugia, coordinated by Prof. Dr. Giorgia Faina.

E-mail: [email protected].

E-mail: [email protected].