Constructions of partial MDS codes over small fields

Partial MDS (PMDS) codes are a class of erasurecorrecting array codes which combine local correction of the rows with global correction of the array. An m×n array code is called an (r; s) PMDS code if each row belongs to an [n,n - r,r + 1] MDS code and the code can correct erasure patterns consisting of r erasures in each row together with s more erasures anywhere in the array. While a recent construction by Calis and Koyluoglu generates (r; s) PMDS codes for all r and s, its field size is exponentially large. In this paper, a family of PMDS codes with field size O (max{m,nr+s}s) is presented.