On Grid Codes

Abstract

If A i is finite alphabet for i = 1, ..., n, the Manhattan distance is defined in n i=1 A i . A grid code is introduced as a subset of n i=1 A i . Alternative versions of the Hamming and Gilbert-Varshamov bounds are presented for grid codes. If A i is a cyclic group for i = 1, ..., n, some bounds for the minimum Manhattan distance of codes that are cyclic subgroups of n i=1 A i are determined in terms of their minimum Hamming and Lee distances. Examples illustrating the main results are provided.