Classification of a family of completely transitive codes

Understand

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.