Portal de Periódicos da CAPES

Giuseppe Veronese and Ernst Witt—neighbours in PG(5,3)

1999; Birkhäuser; Volume: 58; Issue: 1-2 Linguagem: Inglês

10.1007/s000100050095

1420-8903

Hans Havlicek,

Finite Group Theory Research

Dedicated to János Aczél on the occasion of his 75th birthdaySummary.Let P be a point of the Veronese surface V in PG(5, 3).Then there are four conics of V 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 in [6] recently.We give an explicit parametrization of the cap K; the domain is a dual affine plane which arises from PG(2, 3) by removing one point.Thus, as a by-product, we obtain an easy approach to the extended ternary Golay code G12.Finally, we discuss some other procedures that yield 12-sets of points from the Veronese surface.