New Construction of (k + r,k) Systematic MDS Array Codes with r ≤ 4

Abstract

Given a prime L, we present a new construction of (L−1)-dimensional (k+r,k) systematic array codes with r ≤ 4, and concretely characterize sufficient conditions on the selection of L to guarantee the codes’ MDS property. The largest possible k that can be supported by the new MDS array codes is 2L−4, nearly twice as large as that supported by classical MDS array codes such as EVENODD codes and RDP codes. Moreover, the number of XORs per original data bit required in encoding of the new codes asymptotically approaches r with increasing k and L, same as EVENODD codes and RDP codes. In addition, for the case r = 4, the explicit conditions on L we obtain to guarantee the new codes’ MDS property can also be used to guarantee the MDS property of EVENODD codes and RDP codes, but are more general than the well known ones in the literature.