New characterisations of the Nordstrom-Robinson codes

@article{Gillespie2012NewCO,
  title={New characterisations of the Nordstrom-Robinson codes},
  author={Neil I. Gillespie and C. Praeger},
  journal={Bulletin of The London Mathematical Society},
  year={2012},
  volume={49},
  pages={320-330}
}
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 $(15,5)$ respectively. We prove that these codes are also characterised as \emph{completely regular} binary codes with $(m,\delta)=(16,6)$ or $(15,5)$, and moreover, that they are \emph{completely transitive}. Also, it is known that completely transitive codes are necessarily completely regular, but whether… Expand
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