Giuseppe Veronese and Ernst Witt -- Neighbours in PG(5,3)
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arXiv
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| Formato: | Preprint |
| Publicado: |
2012
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| _version_ | 1866929239188570112 |
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| author | Havlicek, Hans |
| author_facet | Havlicek, Hans |
| contents | Let $P$ be a point of the Veronese surface $\Vcal$ in \PG53. Then thereare four conics of $\Vcal$ through $P$. We show that the internal points of those conics form a 12-cap which is a point model for Witt's 5-$(12,6,1)$ design. In fact, this construction is "dual" to a similar construction that has been established by the author. We give an explicit parametrization of the cap $\Kcal$; the domain is a dual affine plane which arises from \PG23 by removing one point. Thus, as a by--product, we obtain an easy approach to the extended ternary Golay code $G_{12}$. Finally, we discuss some other procedures that yield 12-sets of points from the Veronese surface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1210_1926 |
| institution | arXiv |
| publishDate | 2012 |
| record_format | arxiv |
| spellingShingle | Giuseppe Veronese and Ernst Witt -- Neighbours in PG(5,3) Havlicek, Hans Combinatorics 51E22, 05B05 Let $P$ be a point of the Veronese surface $\Vcal$ in \PG53. Then thereare four conics of $\Vcal$ through $P$. We show that the internal points of those conics form a 12-cap which is a point model for Witt's 5-$(12,6,1)$ design. In fact, this construction is "dual" to a similar construction that has been established by the author. We give an explicit parametrization of the cap $\Kcal$; the domain is a dual affine plane which arises from \PG23 by removing one point. Thus, as a by--product, we obtain an easy approach to the extended ternary Golay code $G_{12}$. Finally, we discuss some other procedures that yield 12-sets of points from the Veronese surface. |
| title | Giuseppe Veronese and Ernst Witt -- Neighbours in PG(5,3) |
| topic | Combinatorics 51E22, 05B05 |
| url | https://arxiv.org/abs/1210.1926 |