Isometry Groups of Combinatorial Codes

Abstract

Two isometry groups of combinatorial codes are described: the group of automorphisms and the group of monomial automorphisms, which is the group of those automorphisms that extend to monomial maps. Unlike the case of classical linear codes, where these groups are the same, it is shown that for combinatorial codes the groups can be arbitrary different. Particularly, there exist codes with the full automorphism group and the trivial monomial automorphism group. In the paper the two groups are characterized and codes with predefined isometry groups are constructed.