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Locally repairable codes with multiple repair sets based on packings of block size 4

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Abstract

In distributed storage systems, the utilization of locally repairable codes offers the potential to reduce the complexity and bandwidth required for repairs. This paper focuses on a scenario where each information symbol is associated with several distinct repair sets, each of which includes a single parity check symbol. By leveraging various combinatorial designs, such as resolvable balanced incomplete block designs and resolvable group divisible designs, we establish regular packings and resolvable packings for all alphabet sizes greater than a specified constant. These packings enable the construction of optimal locally repairable codes with multiple repair sets. Specifically, in the case where \(\varvec{r=4}\), we successfully construct optimal locally repairable codes with multiple repair sets, provided that the code dimension k is greater than or equal to 277.

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Acknowledgements

This research is supported by National Natural Science Foundation of China, U2001203, 61871136.

Funding

This research is supported by National Natural Science Foundation of China, U2001203, 61871136.

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Author notes

  1. Han Cai and Linxin Yin are contributed equally to this work.

Authors and Affiliations

  1. School of Information Engineering, Guangdong University of Technology, No. 100, Wai Huan Xi Road, Guangzhou Higher Education Mega Center, Guangzhou, 510006, Guangdong, China

    Xiaopan Han, Guojun Han & Linxin Yin

  2. School of Information Science and Technology, Southwest Jiaotong University, No. 111, North Section 1, Second Ring Road, Chengdu, 610031, Sichuan, China

    Han Cai

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  1. Xiaopan Han
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Contributions

Xiaopan Han: Performed the analysis, collected the data, and wrote the manuscript; Guojun Han: Conceived and designed the analysis, and validated the data; Han Cai: Conceived and designed the analysis, and improved the manuscript. Linxin Yin: Wrote the review and edited the manuscript.

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Correspondence to Guojun Han.

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Han, X., Han, G., Cai, H. et al. Locally repairable codes with multiple repair sets based on packings of block size 4. Cryptogr. Commun. 16, 459–479 (2024). https://doi.org/10.1007/s12095-023-00681-z

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