On cyclic lowest density MDS array codes constructed using starters

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.