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Previous classifications of families of $2$-neighbour-transitive codes leave only those with an affine action on the alphabet to be investigated. Here, $2$-neighbour-transitive codes with minimum distance at least $5$ and that contain \"small\" subcodes as blocks of imprimitivity are classified. 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Praeger, Daniel R. Hawtin, Neil I. Gillespie","submitted_at":"2018-06-27T15:00:23Z","abstract_excerpt":"A code $C$ in the Hamming graph $\\varGamma=H(m,q)$ is $2\\it{\\text{-neighbour-transitive}}$ if ${\\rm Aut}(C)$ acts transitively on each of $C=C_0$, $C_1$ and $C_2$, the first three parts of the distance partition of $V\\varGamma$ with respect to $C$. Previous classifications of families of $2$-neighbour-transitive codes leave only those with an affine action on the alphabet to be investigated. Here, $2$-neighbour-transitive codes with minimum distance at least $5$ and that contain \"small\" subcodes as blocks of imprimitivity are classified. 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