76 citations · 131 across the 17 of their papers we have counts for
21 papers
Parallel window decoding enables scalable fault tolerant quantum computation
Luka Skoric, Dan E. Browne, Kenton M. Barnes +2
Large-scale quantum computers have the potential to hold computational capabilities beyond conventional computers for certain problems. However, the physical qubits within a quantu…
Post-selection-free preparation of high-quality physical qubits
Ben Barber, Neil I. Gillespie, J. M. Taylor
Rapidly improving gate fidelities for coherent operations mean that errors in state preparation and measurement (SPAM) may become a dominant source of error for fault-tolerant oper…
Practical Quantum Computing: The value of local computation
James R. Cruise, Neil I. Gillespie, Brendan Reid
As we enter the era of useful quantum computers we need to better understand the limitations of classical support hardware, and develop mitigation techniques to ensure effective qu…
Equiangular lines, Incoherent sets and Quasi-symmetric designs
Neil I. Gillespie
The absolute upper bound on the number of equiangular lines that can be found in is . Examples of sets of lines that saturate this bound are only known to…
-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…
Conway's groupoid and its relatives
Nick Gill, Neil I. Gillespie, Jason Semeraro +1
In 1997, John Conway constructed a -fold transitive subset of permutations on a set of size for which the subset fixing any given point was isomorphic to the Mathi…
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…
Conway groupoids, regular two-graphs and supersimple designs
Nick Gill, Neil I. Gillespie, Cheryl E. Praeger +1
A design is said to be supersimple if distinct lines intersect in at most two points. From such a design, one can construct a certain subset of Sym$(…
Conway groupoids and completely transitive codes
Nick Gill, Neil I. Gillespie, Jason Semeraro
To each supersimple design one associates a `Conway groupoid,' which may be thought of as a natural generalisation of Conway's Mathieu groupoid associated…
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…
Generating groups using hypergraphs
Nick Gill, Neil I. Gillespie, Anthony Nixon +1
To a set of 4-subsets of a set of size we introduce an invariant called the `hole stabilizer' which generalises a construction of Conway, Elkies and Martin of…
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…