Systematic MDS Array Codes Correcting a Single Criss-Cross Error with Lower Update Complexity

A (k+2,k,m) maximum distance separable (MDS) array code is an array of size m × (k + 2) such that any k out of k +2 columns can retrieve all km information bits. The (k + 2,k,m) array code can correct a single criss-cross error means that the code can retrieve all km information bits if any single column or row is in error. In this paper, we propose new systematic (k + 2,k,m) MDS array codes that can correct a single criss-cross error. In addition, we present efficient decoding algorithms that has lower decoding complexity for any two-row erasures or two-column erasures or one-row plus one-column erasures or one-row error or one-column error. Moreover, we show that our codes have much lower update complexity than that of the existing MDS array codes correcting a single criss-cross error [1].