Algebraic symmetry of codes in hamming graphs

Daniel Hawtin

doi:10.4225/23/5a5808f48f2d0

Algebraic symmetry of codes in hamming graphs

Daniel Hawtin

Research output: Thesis › Doctoral Thesis

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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 language	English
Qualification	Doctor of Philosophy
Awarding Institution	The University of Western Australia
Supervisors/Advisors	Praeger, Cheryl, Supervisor Giudici, Michael, Supervisor Gillespie, Neil Ian, Supervisor
Thesis sponsors	Australian Government Research Training Program
Award date	18 Dec 2017
DOIs	https://doi.org/10.4225/23/5a5808f48f2d0
Publication status	Unpublished - 2017

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10.4225/23/5a5808f48f2d0

THESIS - DOCTOR OF PHILOSOPHY - HAWTIN Daniel Robert - 2017
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Cite this

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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. ",

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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 -

Algebraic symmetry of codes in hamming graphs

Abstract

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