Erased memory page reconstruction using distributed coding for multiple dimensional parities

A method for memory page erasure-correcting property generation in a storage array includes dividing data into multiple stripes for storage in a storage array including multiple storage devices with a topology of a hypercube of a dimension t≥3. The storage devices in same hypercubes of dimension t−1 including the hypercube of dimension t have even parity. An intersection of two non-parallel planes in the hypercube topology is a line, and each point along a line is a storage device in the storage array. Erasure-correcting properties are generated for the data using three nested codes, wherein a first nested code has even parity over planes of class 0, 1 and 2, a second nested code has a first global parity, and a third nested code has a second global parity and a third global parity.