We obtain the Singleton bound for poset block codes and define a maximum distance separable poset block code (MDS $(P,\pi )$-code) as a code meeting this bound. We extend the concept of I-balls to poset block metric and describe r-perfect and MDS $(P,\pi )$-codes in terms of I-perfect codes. As a special case when all the blocks have the same dimension, we establish that MDS $(P,\pi )$-codes are same as I-perfect codes for $I\in {\mathcal{I}}^{\frac{n-k}{m}}(P)$. We show that the duality result also holds for this case. Further, we determine the weight enumerator of an MDS $(P,\pi )$-code.

中文翻译：

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MDS和I-完美的poset分组代码

我们获得用于坐姿分组码的Singleton边界，并定义最大距离可分离的坐姿分组码（MDS $（P，\pi ）$-code）作为符合此限制的代码。我们将I- balls的概念扩展到poset块度量，并描述r- perfect和MDS$（P，\pi ）$-I代码代表I-完美代码。作为所有块具有相同尺寸的特殊情况，我们建立MDS$（P，\pi ）$-代码与我相同-的完美代码$\mathrm{一世}\in {\mathcal{一世}}^{\frac{ñ-ķ}{米}}（P）$。我们证明了对偶结果在这种情况下也成立。此外，我们确定MDS的权重枚举器$（P，\pi ）$-码。