  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.
