  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 the converse holds has up
to now been an open question. We answer this by proving that certain completely
regular codes are not completely transitive, namely, the (Punctured) Preparata
codes other than the (Punctured) Nordstrom-Robinson code.

Combinatorics