On \(k\)-arcs covering a line in finite projective planes. (Q2716024)
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scientific article; zbMATH DE number 1600990
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On \(k\)-arcs covering a line in finite projective planes. |
scientific article; zbMATH DE number 1600990 |
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20 July 2005
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covering arc
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projective plane
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affine plane
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perfect hash family
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On \(k\)-arcs covering a line in finite projective planes. (English)
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Consider a line in a \(\text{PG}(2,q)\). A \(k\)-arc covers the line, if every point of the line lies on a secant of the arc. The authors show that there exist covering \(k\)-arcs with \(k\) approximately \(2\sqrt {\mathstrut q}\), prove \(k \geq (1+\sqrt {8q+9})/2\) and establish when the equality holds. They also connect the notion of covering arcs to the notion of perfect hash families.
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