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

Supervisors/Advisors 

Thesis sponsors  
Award date  18 Dec 2017 
DOIs  
Publication status  Unpublished  2017 
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Algebraic symmetry of codes in hamming graphs. / Hawtin, Daniel.
2017.Research output: Thesis › Doctoral 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 errorcorrecting codes, which have digital, and mathematical, applications. A code consists of strings of a fixed length in some alphabet.A code is 2neighbourtransitive if it satisfies particular symmetry properties. New infinite families of 2neighbourtransitive codes are exhibited, certain subclasses classified, and a full characterisation given in the binary case.A code is selusive 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 errorcorrecting codes, which have digital, and mathematical, applications. A code consists of strings of a fixed length in some alphabet.A code is 2neighbourtransitive if it satisfies particular symmetry properties. New infinite families of 2neighbourtransitive codes are exhibited, certain subclasses classified, and a full characterisation given in the binary case.A code is selusive 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 