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Two classes of optimal LRCs with information (rt)-locality

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Abstract

Locally repairable codes (LRCs) with (rt)-locality have received considerable attention in recent years, since they are able to solve common problems in distributed storage systems such as repairing multiple node failures and managing hot data. Constructing LRCs with excellent parameters becomes an interesting research subject in distributed storage systems and coding theory. In this paper, we present two constructions of LRCs with information (rt)-locality based on linear algebra and partial geometry, respectively. Both constructions generate LRCs with new parameters which are optimal with respect to the bound proposed by Rawat et al. (IEEE Trans Inf Theory 62(8):4481–4493, 2016).

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Acknowledgements

The authors are very grateful to the co-chairs of WCC, Anne Canteaut and Felix Ulmer, and to the anonymous reviewers for their comments and suggestions. Special thanks to Alex Pott for bringing our attention to connection of proposed codes with geometries, we addressed these in Remarks. The authors also would like to thank the reviewers for bringing our attention to the connection of our codes with PIR/batch codes.

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Correspondence to Zhengchun Zhou.

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The work of P. Tan and Z. Zhou was supported in part by the National Natural Science Foundation of China under Grants 61672028 and 11971395, and in part by Doctoral Innovation Fund Program of Southwest Jiaotong University.

V. Sidorenko is on leave from Institute for Information Transmission Problems, Russian Academy of Sciences. His work is supported by the Russian Government (Contract No 14.W03.31.0019).

U. Parampalli is supported in part by the Australian Research Councils Discovery under Grant DP150104473 and in part by the University of Melbourne’s 2014 International Research and Research Training Fund.

This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Coding and Cryptography 2019”.

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Tan, P., Zhou, Z., Sidorenko, V. et al. Two classes of optimal LRCs with information (rt)-locality. Des. Codes Cryptogr. 88, 1741–1757 (2020). https://doi.org/10.1007/s10623-020-00728-9

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  • DOI: https://doi.org/10.1007/s10623-020-00728-9

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