Algebraic symmetry of codes in hamming graphs

Daniel Hawtin

    Research output: ThesisDoctoral Thesis

    337 Downloads (Pure)

    Abstract

    This thesis studies symmetry properties of error-correcting codes, which have digital, and mathematical, applications. A code consists of strings of a fixed length in some alphabet.

    A code is 2-neighbour-transitive if it satisfies particular symmetry properties. New infinite families of 2-neighbour-transitive codes are exhibited, certain subclasses classified, and a full characterisation given in the binary case.

    A code is s-elusive if it exhibits less symmetry than the set of strings at distance s from it. Elusive codes are shown to be related to certain designs, with infinite families of examples provided.

    Finally, possible extensions of the main results are discussed.
    Original languageEnglish
    QualificationDoctor of Philosophy
    Awarding Institution
    • The University of Western Australia
    Supervisors/Advisors
    • Praeger, Cheryl, Supervisor
    • Giudici, Michael, Supervisor
    • Gillespie, Neil Ian, Supervisor
    Thesis sponsors
    Award date18 Dec 2017
    DOIs
    Publication statusUnpublished - 2017

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