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Partial MDS (PMDS) codes are erasure codes combining local (row) correctionwith global additional correction of entries, while Sector-Disk (SD) codes areerasure codes that address the mixed failure mode of current RAID systems. Ithas been an open problem to construct general codes that have the PMDS and theSD properties, and previous work has relied on Monte-Carlo searches. In thispaper, we present a general construction that addresses the case of any numberof failed disks and in addition, two erased sectors. The construction requiresa modest field size. This result generalizes previous constructions extendingRAID~5 and RAID~6.

Construction of Partial MDS (PMDS) and Sector-Disk (SD) Codes with Two Global Parity Symbols