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Codes with respect to weighted poset block metric

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Abstract

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.

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Funding

National Natural Science Foundation of China (Grant Nos. 12171191, 12271199, and 61977036), Hubei Provincial Science and Technology Innovation Base (Platform) Special Project 2020DFH002 (Grant No. 2020DFH002), Fundamental Research Funds for the Central Universities (Grant No. 30106220482).

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Author notes

  1. Wen Ma

    Present address: School of Science, Nanjing Forestry University, Nanjing, 210037, Jiangsu, China

Authors and Affiliations

  1. School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, 430079, Hubei, China

    Jinquan Luo

  2. School of Mathematics and Statistics, Central China Normal University, Wuhan, China

    Wen Ma

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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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Communicated by T. Feng.

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Ma, W., Luo, J. Codes with respect to weighted poset block metric. Des. Codes Cryptogr. 92, 341–363 (2024). https://doi.org/10.1007/s10623-023-01311-8

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