On cyclic lowest density MDS array codes constructed using starters

Abstract

In this paper, we present a systematic study on cyclic lowest density MDS array codes constructed using starters. We first show that all cyclic lowest density MDS array codes of distance 3 and length 2n can be constructed using normalized cyclic bipyramidal starters in the additive group of congruence classes modulo 2n. We then discuss when and how to transform non-cyclic lowest density MDS array codes constructed using other starters (including even starters and patterned starters) to cyclic codes. Finally, we also discuss how to construct quasi-cyclic lowest density MDS array codes using multi-starters for an even length when no cyclic lowest density MDS array code exists for this even length.

Partial-MDS Codes and Their Application to RAID Type of Architectures

“…It is preferrable to use Maximum Distance Separable (MDS) codes for RAID 6 types of architectures: in order to correct two erasures exactly two parities are needed. There are many choices for MDS codes correcting two or more erasures: we can use Reed-Solomon (RS) codes [31] [35], or array codes, like EVENODD [4], RDP [11], X-codes [43], B-codes [42], C-codes [28], Liberation codes [36], and others [5] [39].…”