Finite Geometries

1. Front Matter

   Pages i-x

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2. Point-Line Geometries with a Generating Set that Depends on the Underlying Field

   • R. J. Blok, A. Pasini

   Pages 1-25

3. On a Class of Symmetric Divisible Designs which are Almost Projective Planes

   • Aart Blokhuis, Dieter Jungnickel, Bernhard Schmidt

   Pages 27-34

4. Generalized Elliptic Cubic Curves, Part 1

   • Francis Buekenhout

   Pages 35-48

5. Fixed Points and Cycles

   • Peter J. Cameron

   Pages 49-60

6. RWPRI Geometries for the Alternating Group A ₈

   • Philippe Cara

   Pages 61-97

7. A Characterization of Truncated D _n -Buildings as Flag-Transitive PG.PG*-Geometries

   • I. Cardinali, A. Pasini

   Pages 99-119

8. Group-Theoretic Characterizations of Classical Ovoids

   • A. Cossidente, O. H. King

   Pages 121-131

9. A General Framework for Subexponential Discrete Logarithm Algorithms in Groups of Unknown Order

   • Andreas Enge

   Pages 133-146

10. Generalized Quadrangles and Pencils of Quadrics

    • Dina Ghinelli, Stefan Löwe

    Pages 147-158

11. The Desarguesian Plane of Order Thirteen

    • M. Giulietti, J. W. P. Hirschfeld, G. Korchmáros

    Pages 159-170

12. Two Characterizations of the Hermitian Spread in the Split Cayley Hexagon

    • Eline Govaert, Hendrik Van Maldeghem

    Pages 171-176

13. Epimorphisms of Generalized Polygons, Part 2: Some Existence and Non-Existence Results

    • Ralf Gramlich, Hendrik Van Maldeghem

    Pages 177-200

14. The Packing Problem in Statistics, Coding Theory and Finite Projective Spaces: Update 2001

    • J. W. P. Hirschfeld, L. Storme

    Pages 201-246

15. The Geometric Approach to Linear Codes

    • I. N. Landjev

    Pages 247-256

16. Flocks and Locally Hermitian 1-Systems of Q(6, q)

    • D. Luyckx, J. A. Thas

    Pages 257-275

17. Diagrams for Embeddings of Polygons

    • B. Mühlherr, H. Van Maldeghem

    Pages 277-293

18. The Law—Penttila q-Clan Geometries

    • Stanley E. Payne

    Pages 295-303

19. Implications of Line-Transitivity for Designs

    • Cheryl E. Praeger

    Pages 305-317

20. Exponent Bounds

    • Bernhard Schmidt

    Pages 319-331

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.

• algebra
• algorithms
• coding theory
• finite group
• geometry
• sets
• statistics
• combinatorics

• University of Eindhoven, The Netherlands

  A. Blokhuis

• University of Sussex, England

  J. W. P. Hirschfeld

• University of Augsburg, Germany

  D. Jungnickel

• University of Ghent, Belgium

  J. A. Thas

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