On Grid Codes

02/21/2022

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by   E. J. García-Claro, et al.

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If A_i is finite alphabet for i=1,...,n, the Manhattan distance is defined in ∏_i=1^nA_i. A grid code is introduced as a subset of ∏_i=1^nA_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 ∏_i=1^nA_i are determined in terms of their minimum Hamming and Lee distances. Examples illustrating the main results are provided.