Caps in finite projective spaces of odd order (Q1365034)
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scientific article; zbMATH DE number 1053893
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Caps in finite projective spaces of odd order |
scientific article; zbMATH DE number 1053893 |
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Caps in finite projective spaces of odd order (English)
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13 April 1998
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The authors derive upper bounds for the number of points of complete caps in \(\text{PG} (n,q)\) for \(q\) odd and \(n\geq 3\). More precisely, they use upper bounds on the number of points of the second largest complete cap in \(\text{PG} (i,q)\), \(i=2,3\), to obtain upper bounds for the number of points of a complete cap in \(\text{PG} (i+1,q)\). Then, using a result of \textit{J. F. Voloch} [J. Geom. 38, No. 1/2, 198-200 (1990; Zbl 0707.51010)], one obtains new upper bounds for the number of points on a complete cap in \(\text{PG} (n,P)\), for \(n\geq 3\) and \(p\) prime.
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finite projective space
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\(k\)-arc
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complete caps
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upper bounds
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