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Infinite families of optimal linear codes and their applications to distributed storage systems

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Abstract

Linear codes with large minimum distances perform well in error and erasure corrections. Constructing such linear codes is a main topic in coding theory. In this paper, we propose four families of linear codes which are optimal or distance-optimal with respect to the Griesmer bound. Using the theory of characters over finite fields, we determine the weight distribution of these linear codes. The results show that these linear codes are two-weight codes. Finally, we analyse the locality of these linear codes and present three families of distance-optimal binary locally repairable code with locality 2 or 3.

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Acknowledgements

We are grateful to the anonymous referees and the associate editor for useful comments and suggestions that improved the presentation and quality of this paper.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Hubei Normal University, Huangshi, 435002, China

    Hui Yan & Kezheng Zuo

  2. School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore, 637371, Singapore

    Gaojun Luo

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  1. Hui Yan
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  2. Kezheng Zuo
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  3. Gaojun Luo
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Correspondence to Gaojun Luo.

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This work was supported by the National Natural Science Foundation of China (Grant No. 11961076), the Youth Science Foundation of Hubei Normal University (HS2020QN031)

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Yan, H., Zuo, K. & Luo, G. Infinite families of optimal linear codes and their applications to distributed storage systems. J. Appl. Math. Comput. 68, 4223–4239 (2022). https://doi.org/10.1007/s12190-022-01701-6

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  • DOI: https://doi.org/10.1007/s12190-022-01701-6

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