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Uniqueness of certain completely regular Hadamard codes
TLDR
We classify binary completely regular codes of length m with minimum distance δ for ( m , δ ) = ( 12 , 6 ) and ( 11 , 5 ) and prove that such codes are unique up to equivalence, and in particular, are equivalent to certain Hadamard codes. Expand
Diagonally neighbour transitive codes and frequency permutation arrays
Constant composition codes have been proposed as suitable coding schemes to solve the narrow band and impulse noise problems associated with powerline communication, while at the same timeExpand
New characterisations of the Nordstrom-Robinson codes
In his doctoral thesis, Snover proved that any binary $(m,256,\delta)$ code is equivalent to the Nordstrom-Robinson code or the punctured Nordstrom-Robinson code for $(m,\delta)=(16,6)$ or $(15,5)$Expand
Classification of a family of completely transitive codes
TLDR
This paper studies the subfamily of completely transitive codes in Hamming graphs, those in which an automorphism group is transitive on each part of the distance partition. Expand
SIC-POVMS AND THE STARK CONJECTURES
The existence of a set of d pairwise equiangular complex lines (a SIC-POVM) in ddimensional Hilbert space is currently known only for a finite set of dimensions d. We prove that, if there exists aExpand
Increasing the Minimum Distance of Codes by Twisting
TLDR
Twisted permutation codes, introduced recently by the second and third authors, are frequency permutation arrays that are obtained by a repetition construction applied to a smaller code. Expand
Neighbour transitivity on codes in Hamming graphs
TLDR
This paper examines codes with the property that some group of automorphisms acts transitively on the set of neighbours of the code. Expand
CHARACTERISATION OF A FAMILY OF NEIGHBOUR TRANSITIVE CODES
We consider codes of length m over an alphabet of size q as subsets of the vertex set of the Hamming graph = H(m,q). A code for which there exists an automorphism group X 6 Aut() that actsExpand
Entry-faithful 2-neighbour transitive codes
TLDR
We give a classification of $$2$$2-neighbour transitive codes, with minimum distance $$\delta \geqslant 5$$δ⩾5, for which $$X$$X acts faithfully on the set of entries of the Hamming graph. Expand
Conway Groupoids and Completely Transitive Codes
TLDR
We show that Sp2m(2) naturally occur as Conway groupoids associated to certain designs. Expand
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