A recovery enabling system for storage arrays is a high distance generalization of RAID-5 with optimal update complexity and near optimal storage efficiency. The recovery enabling system utilizes presets, data cells with known values that initialize the reconstruction process. The presets allow resolution of parity equations to reconstruct data when failures occur. In one embodiment, additional copies of the layout of the recovery enabling system are packed onto the same disks to minimize the effect of presets on storage efficiency without destroying the clean geometric construction of the recovery enabling system. The recovery enabling system has efficient XOR-based encoding, recovery, and updating algorithms for arbitrarily large distances, making the recovery enabling system an ideal candidate when storage-efficient reliable codes are required.