Codes with respect to weighted poset block metric

作者：Ma, Wen; Luo, Jinquan^*

来源：Designs, Codes, and Cryptography, 2023.

DOI：10.1007/s10623-023-01311-8

• Linear isometry
• Poset block metric
• Principal ideal
• Pomset block metric
• Weighted poset block metric

We study a new family of metrics, weighted poset block metric, which generalizes the weighted coordinates poset metric introduced by Panek and Pinheiro (IEEE Trans Inf Theory 66(11):6823-6834, 2020) and the metric for linear error-block codes introduced by Feng et al. (Finite Fields Appl 12(4):638-652, 2006). This metric covers various metrics such as Hamming metric, Lee metric, poset metric, pomset metric, poset block metric, pomset block metric and so on. We give a complete description of the groups of linear isometries of these metric spaces in terms of a semi-direct product. Moreover, we obtain a Singleton type bound for codes equipped with weighted poset block metric and define MDS codes. When the poset is a chain, we study the relationship between MDS codes and perfect codes.

• 单位
  南京林业大学