76 citations · 131 across the 17 of their papers we have counts for
13 papers · 1 filter
-Neighbour-Transitive Codes with Small Blocks of Imprimitivity
Neil I. Gillespie, Daniel R. Hawtin, Cheryl E. Praeger
A code in the Hamming graph is if acts transitively on each of , and , the first three…
Construction of the outer automorphism of S6 via a complex Hadamard matrix
Neil Gillespie, Padraig Ó Catháin, Cheryl Praeger
We give a new construction of the outer automorphism of the symmetric group on six points. Our construction features a complex Hadamard matrix of order six containing third roots o…
Alphabet-Almost-Simple 2-Neighbour Transitive Codes
Neil I. Gillespie, Daniel R. Hawtin
Let be a subgroup of the full automorphism group of the Hamming graph , and a subset of the vertices of the Hamming graph. We say that is an \emph{-neigh…
Increasing the minimum distance of codes by twisting
Marzieh Akbari, Neil I. Gillespie, Cheryl E. Praeger
Twisted permutation codes, introduced recently by the second and third authors, are frequency permutation arrays. They are similar to repetition permutation codes, in that they are…
Characterisation of a family of neighbour transitive codes
Neil I. Gillespie, Cheryl E. Praeger
We consider codes of length over an alphabet of size as subsets of the vertex set of the Hamming graph . A code for which there exists an automorphism group $X\le…
Twisted Permutation Codes
Neil I. Gillespie, Cheryl E. Praeger, Pablo Spiga
We introduce twisted permutation codes, which are frequency permutation arrays analogous to repetition permutation codes, namely, codes obtained from the repetition construction ap…
A note on binary completely regular codes with large minimum distance
Neil I. Gillespie
We classify all binary error correcting completely regular codes of length with minimum distance .
Elusive Codes in Hamming Graphs
Daniel R. Hawtin, Neil I. Gillespie, Cheryl E. Praeger
We consider a code to be a subset of the vertex set of a Hamming graph. We examine elusive pairs, code-group pairs where the code is not determined by knowledge of its set of neigh…
Classification of a family of completely transitive codes
Neil I. Gillespie, Michael Giudici, Cheryl E. Praeger
The completely regular codes in Hamming graphs have a high degree of combinatorial symmetry and have attracted a lot of interest since their introduction in 1973 by Delsarte. This…
New characterisations of the Nordstrom-Robinson codes
Neil I. Gillespie, Cheryl E. Praeger
In his doctoral thesis, Snover proved that any binary code is equivalent to the Nordstrom-Robinson code or the punctured Nordstrom-Robinson code for or $…
Diagonally Neighbour Transitive Codes and Frequency Permutation Arrays
Neil I. Gillespie, Cheryl E. Praeger
Constant composition codes have been proposed as suitable coding schemes to solve the narrow band and impulse noise problems associated with powerline communication. In particular,…
Neighbour transitivity on codes in Hamming graphs
Neil I. Gillespie, Cheryl E. Praeger
We consider a \emph{code} to be a subset of the vertex set of a \emph{Hamming graph}. In this setting a \emph{neighbour} of the code is a vertex which differs in exactly one entry…
Uniqueness of certain completely regular Hadamard codes
Neil I. Gillespie, Cheryl E. Praeger
We classify binary completely regular codes of length with minimum distance for and . We prove that such codes are unique up to equivalence, and in p…