Sector-disk codes and partial MDS codes with up to three global parities

A new construction for sector-disk codes and partial MDS codes up to three sector erasures are proposed. In contrast to existing codes, which are based on the design of parity check matrix, our new code is based on the design of generator matrix. This new approach allows us to construct a code that requires a small field size. In particular, for the case when there is only one sector erasure, our field size requirement is independent of the number of sectors and is close to optimal. For the case when there are three sector erasures, we provide a condition which allows the code be constructed by computer search.