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MDS and I-perfect poset block codes
Finite Fields and Their Applications ( IF 1.2 ) Pub Date : 2019-12-10 , DOI: 10.1016/j.ffa.2019.101620
B.K. Dass , Namita Sharma , Rashmi Verma

We obtain the Singleton bound for poset block codes and define a maximum distance separable poset block code (MDS (P,π)-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,π)-codes in terms of I-perfect codes. As a special case when all the blocks have the same dimension, we establish that MDS (P,π)-codes are same as I-perfect codes for IInkm(P). We show that the duality result also holds for this case. Further, we determine the weight enumerator of an MDS (P,π)-code.



中文翻译:

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 Pπ-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MDSPπ-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MDSPπ-代码与相同-的完美代码一世一世ñ-ķP。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Pπ-码。

更新日期:2019-12-10
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