The sizes \(k\) of the complete \(k\)-caps in \(PG(n,q)\), for small \(q\) and \(3\leq n \leq 5\) (Q2713653)
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scientific article; zbMATH DE number 1602781
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The sizes \(k\) of the complete \(k\)-caps in \(PG(n,q)\), for small \(q\) and \(3\leq n \leq 5\) |
scientific article; zbMATH DE number 1602781 |
Statements
10 June 2001
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cap
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complete cap
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finite projective space
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The sizes \(k\) of the complete \(k\)-caps in \(PG(n,q)\), for small \(q\) and \(3\leq n \leq 5\) (English)
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A \(k\)-cap in \(PG(n,q)\) is a set of \(k\)-points, no three of which are collinear. A \(k\)-cap in \(PG(n,q)\) is called complete, if it is not contained by a \((k+1)\)-cap in \(PG(n,q)\). The paper reports results of a computer search for sizes of complete \(k\)-caps. The spectrum of sizes (i.e. the possible values of \(k\)) has been determined for \((n,q) \in \{(3,2),(3,3),(3,4),(3,5),(4,2),(4,3),(5,2)\}\). The connection to \([n,n-k,4]\)-codes over \(GF(q)\) is mentioned as the motivation for the paper.
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