Codes in Johnson graphs associated with quadratic forms over F2

Mark Ioppolo

Research output: ThesisDoctoral Thesis

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Abstract

This thesis studies strongly incidence-transitive codes in Johnson graphs associated with the 2-transitive actions of Sp(2n,2) of
degrees 22n-1±2n-1. We construct two new infinite families of strongly incidence-transitive codes and demonstrate that they are
the only examples with codeword stabilisers contained in a geometric Aschbacher class. We construct two additional examples
using the fully deleted permutation modules for the symmetric group Sm with m=10 and show no further examples arise for
other values of m. If a codeword stabiliser is almost-simple then we show in most cases that the corresponding code cannot be
strongly incidence-transitive, though several possibilities remain open.
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • The University of Western Australia
Thesis sponsors
Award date10 Mar 2020
DOIs
Publication statusUnpublished - 2019

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