Small Complete Caps in Spaces of Even Characteristic

✍ Scribed by F. Pambianco; L. Storme

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 652 KB
• Volume: 75
• Category: Article
• ISSN: 0097-3165
• DOI: 10.1006/jcta.1996.0064

✦ Synopsis

In 1959, Segre constructed a complete (3q+2)-cap in PG(3, q), q even. This showed that the size of the smallest complete k-cap in PG(3, q), q even, is almost equal to the trivial lower bound which is of order -2q. Generalizing the construction of Segre, complete (q n +3(q n&1 + } } } +q)+2)-caps in PG(2n, q), q even, q 4, and complete (3(q n + } } } +q)+2)-caps in PG(2n+1, q), q even, q 4, are constructed. This shows that in all spaces PG(2n+1, q), q even, the size of the smallest complete k-cap is almost equal to the trivial lower bound which is of order -2 q n .