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Constructions of Codes with Weighted Poset Block Metrics

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Abstract

Weighted poset block metric is a generalization of two types of metrics: one is weighted poset metric introduced by Panek and Pinheiro (2010) and the other is metric for linear error-block codes introduced by Feng and Hickernell (2006). 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 studied.

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Funding

National Natural Science Foundation of China (Nos. 12171191, 12271199) and self-determined research funds of CCNU from the colleges’ basic research and operation of MOE (no. CCNU22JC001).

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Authors and Affiliations

  1. School of Science, Nanjing Forestry University, 210037, Nanjing, Jiangsu, China

    Wen Ma

  2. School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, China

    Jinquan Luo

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  1. Wen Ma
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  2. Jinquan Luo
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Correspondence to Jinquan Luo.

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Ma, W., Luo, J. Constructions of Codes with Weighted Poset Block Metrics. Order (2024). https://doi.org/10.1007/s11083-024-09665-x

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