## Finite Geometries: Proceedings of the Fourth Isle of Thorns ConferenceAart Blokhuis, James W.P. Hirschfeld, Dieter Jungnickel, Joseph A. Thas When? These are the proceedings of Finite Geometries, the Fourth Isle of Thorns Conference, which took place from Sunday 16 to Friday 21 July, 2000. It was organised by the editors of this volume. The Third Conference in 1990 was published as Advances in Finite Geometries and Designs by Oxford University Press and the Second Conference in 1980 was published as Finite Geometries and Designs by Cambridge University Press. The main speakers were A. R. Calderbank, P. J. Cameron, C. E. Praeger, B. Schmidt, H. Van Maldeghem. There were 64 participants and 42 contributions, all listed at the end of the volume. Conference web site http://www. maths. susx. ac. uk/Staff/JWPH/ Why? This collection of 21 articles describes the latest research and current state of the art in the following inter-linked areas: • combinatorial structures in finite projective and affine spaces, also known as Galois geometries, in which combinatorial objects such as blocking sets, spreads and partial spreads, ovoids, arcs and caps, as well as curves and hypersurfaces, are all of interest; • geometric and algebraic coding theory; • finite groups and incidence geometries, as in polar spaces, gener alized polygons and diagram geometries; • algebraic and geometric design theory, in particular designs which have interesting symmetric properties and difference sets, which play an important role, because of their close connections to both Galois geometry and coding theory. |

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### Contents

II | 1 |

III | 27 |

IV | 35 |

V | 49 |

VI | 61 |

VII | 99 |

VIII | 121 |

IX | 133 |

XIV | 201 |

XV | 247 |

XVI | 257 |

XVII | 277 |

XVIII | 295 |

XIX | 305 |

XX | 319 |

XXI | 333 |

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### Common terms and phrases

abelian acts Algebra algorithm arcs associated assume automorphism belong blocking sets bound building called caps classical codes collinear Combin complete Computer condition conic consider construction contained contradiction corresponding cubic curves defined denote designs determine diagram difference sets distance distinct elements elliptic embedding equal Equation examples exists fact field finite fixed flag GECC geometry give given group G Hence hexagon holds hyperplane implies incident inductively infinite integer intersection isomorphic known least Lemma linear Math matrix minimal geometries normal Note obtain ovoid pair parameters particular partition pencil permutation PG(n plane points polar polygons prime problem projective space Proof prove quadrangles quadric rank regular relation Remark respect result satisfying spread square stabilizer structure subgroup subspace Suppose symmetry Table Thas Theorem Theory transitive unique University values