If $A_{i}$ is finite alphabet for $i=1,...,n$, the Manhattan distance is defined in $\prod_{i=1}^{n}A_{i}$. A grid code is introduced as a subset of $\prod_{i=1}^{n}A_{i}$. 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 $\prod_{i=1}^{n}A_{i}$ are determined in terms of their minimum Hamming and Lee distances. Examples illustrating the main results are provided.
翻译：如果$A[i]$是美元=1,...n$的固定字母,曼哈顿距离的定义是$\prod ⁇ i=1 ⁇ n}A ⁇ i}$。输入网格代码作为$\ prod ⁇ i=1 ⁇ n}A ⁇ i$的子集。哈明和吉尔伯特-瓦尔沙莫夫界限的替代版本被显示为网格代码。如果$A ⁇ }是一个环形组,1美元=1,n$,一些曼哈顿最起码距离的代码的界限是$\prod ⁇ i=1 ⁇ n}A ⁇ }美元,这些代码的周期分组以其最小的Hamming和Lee距离确定。提供了主要结果的示例。
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