Partial MDS (PMDS) and sector-disk (SD) codes are classes of erasure correcting codes that combine locality with strong erasure correction capabilities. We construct PMDS and SD codes where each local code is a bandwidth-optimal regenerating MDS code. In the event of a node failure, these codes reduce both, the number of servers that have to be contacted as well as the amount of network traffic required for the repair process. The constructions require significantly smaller field size than the only other construction known in literature. Further, we present a PMDS code construction that allows for efficient repair for patterns of node failures that exceed the local erasure correction capability of the code and thereby invoke repair across different local groups.

中文翻译：

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带再生的部分 MDS 代码

部分 MDS (PMDS) 和扇区磁盘 (SD) 代码是将局部性与强大的擦除校正能力相结合的擦除校正代码类别。我们构建 PMDS 和 SD 代码，其中每个本地代码都是带宽最优的再生 MDS 代码。如果节点发生故障，这些代码会减少必须联系的服务器数量以及修复过程所需的网络流量。与文献中已知的唯一其他结构相比，这些结构需要明显更小的区域尺寸。此外，我们提出了一种 PMDS 代码构造，它允许对超出代码的本地擦除纠正能力的节点故障模式进行有效修复，从而跨不同本地组调用修复。