Erased memory page reconstruction using distributed coding for multiple dimensional parities

A computer program product for memory page erasure reconstruction in a storage array, the computer program product comprising a computer readable storage medium having program instructions embodied therewith, the program instructions executable by a processor to cause the processor to:

• divide, by the processor, data into a plurality of stripes for storage in a storage array comprising a plurality of storage devices with a topology of a hypercube of a dimension t≥3 wherein the storage devices in same hypercubes of dimension t−1 comprising 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;
• and
• reconstruct, by the processor, erased data for erased memory pages from non-erased data in the storage array by using parities in at least three dimensions based on the hypercube topology of the storage devices.