Designs in Finite Geometry

Research output: ThesisDoctoral Thesis

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Abstract

This thesis is concerned with the study of Delsarte designs in symmetric association schemes, particularly in the context of finite geometry. We construct an infinite family of hemisystems of the parabolic quadrics Q(2d, q) for q an odd prime power, and d at least 2. We consider how one might constrain the strata or the size of a design using Krein parameters, and explore the construction of "witnesses" to the non-existence of designs. We show that m-ovoids of certain regular near polygons must be hemisystems. We also introduce strong semi-canonicity for more efficient computation, and obtain various new computational results.
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • The University of Western Australia
Supervisors/Advisors
  • Bamberg, John, Supervisor
  • Niemeyer, Alice, Supervisor
  • Royle, Gordon, Supervisor
Thesis sponsors
Award date15 Dec 2020
DOIs
Publication statusUnpublished - 2020

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