Neil I. Gillespie, Michael Giudici, Cheryl E. Praeger
Published 2012-08-02, updated 2012-10-26Version 2
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 paper studies the subfamily of completely transitive codes, those in which an automorphism group is transitive on each part of the distance partition. This family is a natural generalisation of the binary completely transitive codes introduced by Sole in 1990. We take the first step towards a classification of these codes, determining those for which the automorphism group is faithful on entries.
The automorphism groups of Johnson graphs revisited
On the Automorphism Group of a Graph
On the Classification of Extremal Doubly Even Self-Dual Codes with 2-Transitive Automorphism Group
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