Isometry groups of combinatorial codes

Two isometry groups of a combinatorial code C are described: the group Iso(C) of isometries of a code to itself and the group Mon(C) of isometries of a code to itself 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 a code with the richest possible group Iso(C) and the trivial group Mon(C). The characterization of the groups and the construction of codes with predefined isometry groups are given.