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- W4367393617 abstract "Locally repairable codes (LRCs) have recently been widely used in distributed storage systems and the LRCs with $(r,delta)$-locality ($(r,delta)$-LRCs) attracted a lot of interest for tolerating multiple erasures. Ge et al. constructed $(r,delta)$-LRCs with unbounded code length and optimal minimum distance when $delta+1 leq d leq 2delta$ from the parity-check matrix equipped with the Vandermonde structure, but the block length is limited by the size of $mathbb{F}_q$. In this paper, we propose a more general construction of $(r,delta)$-LRCs through the parity-check matrix. Furthermore, with the help of MDS codes, we give three classes of explicit constructions of optimal $(r,delta)$-LRCs with block length beyond $q$. It turns out that 1) our general construction extends the results of Ge et al. and 2) our explicit constructions yield some optimal $(r,delta)$-LRCs with new parameters." @default.
- W4367393617 created "2023-04-30" @default.
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- W4367393617 date "2023-04-27" @default.
- W4367393617 modified "2023-09-26" @default.
- W4367393617 title "Explicit Constructions of Optimal $(r,delta)$-Locally Repairable Codes" @default.
- W4367393617 doi "https://doi.org/10.48550/arxiv.2304.14011" @default.
- W4367393617 hasPublicationYear "2023" @default.
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