Locally repairable codes are desirable for distributed storage systems to improve the repair efficiency. In this paper, a new combination of codes with locality and codes with multiple disjoint repair sets (also called availability) is introduced. Accordingly, a Singleton-type bound is derived for the new code, which contains those bounds in [9], [20], [28] as special cases. Optimal constructions are proposed with respect to the new bound. In addition, these constructions can also generate optimal codes with multiple disjoint repair sets with respect to the bound in [28], which to the best of our knowledge, are the first explicit constructions that can achieve the bound in [28].

中文翻译：

---

具有多个不相交修复集的最优局部可修复码

分布式存储系统需要本地可修复代码以提高修复效率。在本文中，介绍了具有局部性的代码和具有多个不相交修复集（也称为可用性）的代码的新组合。因此，为新代码派生了一个单例类型的边界，其中包含在[9], [20], [28]作为特殊情况。针对新边界提出了最佳构造。此外，这些构造还可以生成具有多个不相交修复集的最优代码，这些修复集相对于[28]，据我们所知，这是第一个可以在 [28].