Groups of linear isometries on weighted poset block spaces
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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. [(<ref>)] and the metric for linear error-block codes introduced by Feng et al. [(<ref>)]. 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.
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