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The distance-3 cyclic lowest-density MDS array code (called the C-Code) is agood candidate for RAID 6 because of its optimal storage efficiency, optimalupdate complexity, optimal length, and cyclic symmetry. In this paper, theunderlying connections between C-Codes (or quasi-C-Codes) and starters in grouptheory are revealed. It is shown that each C-Code (or quasi-C-Code) of length$2n$ can be constructed using an even starter (or even multi-starter) in$(Z_{2n},+)$. It is also shown that each C-Code (or quasi-C-Code) has a twinC-Code (or quasi-C-Code). Then, four infinite families (three of which are new)of C-Codes of length $p-1$ are constructed, where $p$ is a prime. Besides thefamily of length $p-1$, C-Codes for some sporadic even lengths are alsopresented. Even so, there are still some even lengths (such as 8) for whichC-Codes do not exist. To cover this limitation, two infinite families (one ofwhich is new) of quasi-C-Codes of length $2(p-1)$ are constructed for theseeven lengths.

C-Codes: Cyclic Lowest-Density MDS Array Codes Constructed Using Starters for RAID 6