Algebraic symmetry of codes in hamming graphs

Daniel Hawtin

    Research output: ThesisDoctoral Thesis

    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.
    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
    StateUnpublished - 2017

    Fingerprint

    Hamming Graph
    Symmetry
    Strings
    Error-correcting Codes
    Binary

    Cite this

    @phdthesis{19ab7fbd96f74de38f5633cbf5508832,
    title = "Algebraic symmetry of codes in hamming graphs",
    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.",
    keywords = "Error correction, Group actions, Hamming graph, Neighbour transitive, Completely transitive, Coding theory, Permutation groups",
    author = "Daniel Hawtin",
    year = "2017",
    doi = "10.4225/23/5a5808f48f2d0",
    language = "English",
    school = "The University of Western Australia",

    }

    Hawtin, D 2017, 'Algebraic symmetry of codes in hamming graphs', Doctor of Philosophy, The University of Western Australia. DOI: 10.4225/23/5a5808f48f2d0

    Algebraic symmetry of codes in hamming graphs. / Hawtin, Daniel.

    2017.

    Research output: ThesisDoctoral Thesis

    TY - THES

    T1 - Algebraic symmetry of codes in hamming graphs

    AU - Hawtin,Daniel

    PY - 2017

    Y1 - 2017

    N2 - 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.

    AB - 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.

    KW - Error correction

    KW - Group actions

    KW - Hamming graph

    KW - Neighbour transitive

    KW - Completely transitive

    KW - Coding theory

    KW - Permutation groups

    U2 - 10.4225/23/5a5808f48f2d0

    DO - 10.4225/23/5a5808f48f2d0

    M3 - Doctoral Thesis

    ER -