Repair-optimal parity code

Two parities are generated using repair-optimal maximum-distance-separable (MDS) code, eg. Monarch code. First parity P1 (530) has three parts. First part 532 is a horizontal parity generated by XOR-ing data elements in the same row of content stores 502-508. Second and third parts 534, 536 are based on orthogonal permutations of content from the content stores, e.g. butterfly code, and update the first part. Second part is based, for example, on subset 508, while the third part on subsets 502-506. Second parity P2 (540) has two parts: the first (542) is an orthogonal permutation of content stores 502-508 where contributions of 508 to correcting factors are omitted. The second (544) updates 542 and comprises a subset, e.g. even row selection, of the data elements used for the second and third parts of P1. The problem of using less of remaining data to repair from failures of data storages is addressed.