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Locally repairable codes from combinatorial designs

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Abstract

Locally repairable codes (LRCs) were proposed to reduce the repair degree in distributed storage systems. In particular, LRCs with availability are highly desirable for distributed storage systems, since this kind of codes provide the mechanism of local repair for code symbols and parallel reading of hot data. In this paper, we propose four types of (n, k, r, t)q LRCs from combinatorial designs. We introduce several constructions of LRCs with strict availability and some constructions of distance-optimal LRCs with information-symbol locality. Most of our constructions in this paper are over \({\mathbb{F}_2}\), i.e., they are suitable for implementation.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 61672166), Plan of Shanghai Excellent Academic Leaders (Grant No. 16XD1400200), Innovation Plan of Shanghai Science and Technology (Grant No. 16JC1402700) and Shanghai Leading Talent Programmes.

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Correspondence to Haibin Kan.

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Supporting information

Appendix A. The supporting information is available online at info.scichina.com and link. springer.com. The supporting materials are published as submitted, without typesetting or editing. The responsibility for scientific accuracy and content remains entirely with the authors.

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Zhang, Y., Kan, H. Locally repairable codes from combinatorial designs. Sci. China Inf. Sci. 63, 122304 (2020). https://doi.org/10.1007/s11432-019-2649-5

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Keywords

  • locally repairable codes
  • erasure codes
  • combinatorial designs
  • distributed storage systems
  • codes with availability