Constructions of Partial MDS Codes over Small Fields

Partial MDS (PMDS) codes are a class of erasure-correcting array codes that combine local correction of the rows with global correction of the array. An m× n array code is called an (rs) 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\left (max m, nr+ss}\right) is presented for the case where r= O(1), s= O(1).