Blocking sets of small size and colouring in finite affine planes
Let<em> (S, L) </em>be an either linear or semilinear space and<em> X ⊂ S</em>. Starting from <em>X</em> we define three types of colourings of the points of <em>S</em>. We characterize the Steiner systems<em> S(2, k, ν)</em> which have a c...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Università degli Studi di Catania
1997-11-01
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| Series: | Le Matematiche |
| Online Access: | http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/420 |
| Summary: | Let<em> (S, L) </em>be an either linear or semilinear space and<em> X ⊂ S</em>. Starting from <em>X</em> we define three types of colourings of the points of <em>S</em>. We characterize the Steiner systems<em> S(2, k, ν)</em> which have a colouring of the first type with <em>X = {P}</em>. By means of such colourings we construct blocking sets of small size in affine planes of order <em>q</em>. In particular, from the second and third type of colourings we get blocking sets<em> B</em> with<em> |B| ≤ 2q − 2.</em><br /> |
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| ISSN: | 0373-3505 2037-5298 |