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Optimal minimal linear codes from posets

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Abstract

Recently, some infinite families of minimal and optimal binary linear codes were constructed from simplicial complexes by Hyun et al. We extend this construction method to arbitrary posets. Especially, anti-chains are corresponded to simplicial complexes. In this paper, we present two constructions of binary linear codes from hierarchical posets of two levels. In particular, we determine the weight distributions of binary linear codes associated with hierarchical posets with two levels. Based on these results, we also obtain some optimal and minimal binary linear codes not satisfying the condition of Ashikhmin–Barg.

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Acknowledgements

This research was supported by the National Natural Science Foundation of China (No. 61772015), the Foundation of Science and Technology on Information Assurance Laboratory (No. KJ-17-010), the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (NRF-2017R1D1A1B05030707), and the Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education (No. 2015049582). Part of this work was done when Yansheng Wu was visiting Korea Institute for Advanced Study (KIAS), Seoul, South Korea. Yansheng Wu would like to thank the institution for the kind hospitality. The authors are very grateful to the reviewers and the Editor for their valuable comments and suggestions to improve the quality of this paper. The authors contribute equally to this paper.

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Authors and Affiliations

  1. Konkuk University, Glocal Campus 268 Chungwon-daero, Chungju-si, Chungcheongbuk-do, 27478, South Korea

    Jong Yoon Hyun

  2. Pohang University of Science and Technology, 77 Cheongam-ro, Nam-Gu, Pohang, 37673, South Korea

    Hyun Kwang Kim

  3. School of Computer Science, Nanjing University of Posts and Telecommunications, Nanjing, 210023, P. R. China

    Yansheng Wu

  4. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211100, Jiangsu, P. R. China

    Qin Yue

  5. State Key Laboratory of Cryptology, P. O. Box 5159, Beijing, 100878, P. R. China

    Qin Yue

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  1. Jong Yoon Hyun
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  2. Hyun Kwang Kim
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  3. Yansheng Wu
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  4. Qin Yue
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Correspondence to Qin Yue.

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Communicated by J.-L. Kim.

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Hyun, J.Y., Kim, H.K., Wu, Y. et al. Optimal minimal linear codes from posets. Des. Codes Cryptogr. 88, 2475–2492 (2020). https://doi.org/10.1007/s10623-020-00793-0

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  • DOI: https://doi.org/10.1007/s10623-020-00793-0

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