Families of completely transitive codes and distance transitive graphs

In a previous work, the authors found new families of linear binary completely regular codes with covering radius ρ , where ρ ∈ { 3 , 4 } . In this paper, the automorphism groups of such codes are computed and it is proven that the codes are not only completely regular, but also completely transitive. From these completely transitive codes, in the usual way, i.e., as coset graphs, new presentations of infinite families of distance transitive coset graphs of diameter three and four, respectively, are constructed.