The concept of a locally repairable code (LRC) was introduced to protect the data from disk failures in large-scale storage systems. In this paper, we consider the LRCs with multiple disjoint repair sets and each repair set contains exactly one check symbol. By using several structures from combinatorial design theory, such as balanced incomplete block design, cyclic packing, group divisible design, near-Skolem sequence and Langford sequence, we construct several infinite classes of LRCs with the size of each repair set at most 3, which are optimal with respect to the bound proposed by Rawat et al. in 2016.

中文翻译：

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max（R）= 3 $ \ max \ limits {{R}} = 3 $的常规（k，R，1）装箱及其本地可修复代码

引入了本地可修复代码（LRC）的概念，以保护数据免于大规模存储系统中的磁盘故障。在本文中，我们考虑具有多个不相交修复集的LRC，每个修复集仅包含一个校验符号。通过使用组合设计理论中的几种结构，例如平衡的不完全块设计，循环堆积，组可整分设计，近斯科姆序列和兰福德序列，我们构造了多个无限类的LRC，每个修复集的大小最多为3，这相对于Rawat等人提出的边界而言，最优解是最优的。在2016年。