Codes with Weighted Poset Block Metrics

Abstract: Weighted poset block metric is a generalization of weighted poset metric introduced by Panek et al. ([\ref{panek}]) and the metric for linear error-block codes introduced by Feng et al. ([\ref{FENG}]). This type of metrics includes many classical metrics such as Hamming metric, Lee metric, poset metric, pomset metric, poset block metric, pomset block metric and so on. In this work, we focus on constructing new codes under weighted poset block metric from given ones. Some basic properties such as minimum distance and covering radius are determined.