Completely transitive codes in Hamming graphs
A code \(C\) in the graph \(\Gamma\) is a non-empty subset of the vertex set \(V\) of \(\Gamma\). Completely transitive codes are a special class of completely regular codes. A code in the graph \(\Gamma\) is called a completely transitive code if there exists a subgroup \(G\) of the group of automorphisms of \(\Gamma\), such that each cell \(C_i\) in the distance partition of \(C\) is an orbit of \(G\). The authors consider completely transitive codes in Hamming graphs. The vertices of the Hamming graph \(H(m,q)\) are the \(m\)-tuples with entries from a set \(Q\) of size \(q\). Two vertices are joined by an edge iff they differ in exactly one entry. The authors prove a structure theorem which shows that completely transitive codes are made up of either transitive or nearly complete, completely transitive codes.
scientific article; zbMATH DE number 1382657