2023/03/03 by W. Ma, J. Luo, Ma, W. +1
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #graph theory and CDMA systems #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.2303.01719
In this paper, we introduce a new family of metrics, weighted poset block metric, that combine the weighted coordinates poset metric introduced by Panek et al. [(\refpanek)] and the metric for linear error-block codes introduced by Feng et al. [(\refFENG)]. This type of metrics include many classical 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. Furthermore, we obtain a Singleton type bound for codes equipped with weighted poset block metric and define MDS codes. As a special case when the poset is a chain, we show that MDS codes are equivalent to perfect codes.