Locality enables storage systems to recover failed nodes from small subsets of surviving nodes. The setting where nodes are partitioned into subsets, each allowing for local recovery, is well understood. In this work we consider a generalization introduced by Gopalan et al., where, viewing the codewords as arrays, constraints are imposed on the columns and rows in addition to some global constraints. Specifically, we present a generic method of adding such global parity-checks and derive new results on the set of correctable erasure patterns. Finally, we relate the set of correctable erasure patterns in the considered topology to those correctable in tensor-product codes.

翻译：本地化使存储系统能够从幸存节点的小型子集中恢复失败的节点。 节点被分割成子集的设置非常清楚, 每个节点都允许局部恢复。 在这项工作中,我们认为Gopalan 等人提出的概括化,其中将代码词视为数组,除了一些全球限制外,还对列和行施加了限制。 具体地说, 我们提出了一个通用方法, 添加这样的全球对等检查, 并在一套可纠正的删除模式上得出新的结果 。 最后, 我们把一套可纠正的、 可纠正的地形学模式与那些在高产品代码中可以纠正的模式联系起来 。