Designs in Finite Geometry

Jesse Lansdown

doi:10.26182/krb6-kk43

Designs in Finite Geometry

Jesse Lansdown

Research output: Thesis › Doctoral 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 language	English
Qualification	Doctor of Philosophy
Awarding Institution	The University of Western Australia
Supervisors/Advisors	Bamberg, John, Supervisor Niemeyer, Alice, Supervisor Royle, Gordon, Supervisor
Thesis sponsors	Australian Government Research Training Program
Award date	15 Dec 2020
DOIs	https://doi.org/10.26182/krb6-kk43
Publication status	Unpublished - 2020

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10.26182/krb6-kk43

THESIS - DOCTOR OF PHILOSOPHY - LANSDOWN, Jesse William - 2020
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Cite this

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N2 - 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.

AB - 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.

KW - finite geometry

KW - Delsarte design

KW - association scheme

KW - hemisystem

KW - Krein parameters

KW - polar space

U2 - 10.26182/krb6-kk43

DO - 10.26182/krb6-kk43

M3 - Doctoral Thesis

ER -

Designs in Finite Geometry

Abstract

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