Tilings of the plane and codes for translational combinatorial metrics

A combinatorial metric generalizes the majority of metrics which have been considered in coding theory. Let code words be q-ary n×n-matrices and a translational combinatorial metric be defined by a template T. We assume that one error can corrupt a code word´s elements inside any translation of the template T. If the template T tiles the plane then the code with a certain distance d in the combinatorial metric can be constructed by special interleaving of codes with the same distance d in Hamming metric. Some optimal codes can be obtained using the construction