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New upper bounds and constructions of multi-erasure locally recoverable codes

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Abstract

Multi-erasure locally recoverable codes (ME-LRCs) are an important class of locally recoverable codes (LRCs) with more constraints on the parameters. In this work, we present a new upper bound for ME-LRCs, which is tighter than that proposed by Cadambe and Mazumdar. The technique is to utilize the largest possible weight of linear codes to control the minimum distance. In addition, we present explicit constructions of ME-LRCs to achieve the proposed bound.

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Acknowledgements

The authors thank the anonymous reviewers’ valuable comments, which essentially improve the quality of the paper.

Funding

This work was supported in part by the National Natural Science Foundation of China (Grant No. 62032009, 61902149), the Natural Science Foundation of Guangdong Province (Grant No. 2020A1515010393), and the Major Program of Guangdong Basic and Applied Research (Grant No. 2019B030302008).

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Authors and Affiliations

  1. College of Information Science and Technology/Cyber Security, Jinan University, Guangzhou, Guangdong Province, 510632, China

    Fagang Li, Hao Chen, Huimin Lao & Shanxiang Lyu

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  1. Fagang Li
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  2. Hao Chen
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  3. Huimin Lao
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  4. Shanxiang Lyu
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Contributions

F. Li: writing-original draft. H. Chen: Conceptualization. H. Lao: formal analysis. S. Lyu: writing-review & editing.

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Correspondence to Shanxiang Lyu.

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Fagang Li, Hao Chen, Huimin Lao, and Shanxiang Lyu(corresponding author) are with the College of Information Science and Technology/Cyber Security, Jinan University, Guangzhou, Guangdong Province, 510632, China (e-mail: lifagang13@mails.ucas.ac.cn, haochen@jnu.edu.cn, laohuimin@stu2018.jnu.edu.cn, lsx07@jnu.edu.cn).

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Li, F., Chen, H., Lao, H. et al. New upper bounds and constructions of multi-erasure locally recoverable codes. Cryptogr. Commun. 15, 513–528 (2023). https://doi.org/10.1007/s12095-022-00618-y

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