Minimal-density, RAID-6 Codes: An Approach for w = 9

RAID-6 erasure codes provide vital data integrity in modern storage systems. There is a class of RAID-6 codes called “Minimal Density Codes,” which have desirable performance properties. These codes are parameterized by a “word size,” w, and constructions of these codes are known when w and w + 1 are prime numbers. However, there are obvious gaps for which there is no theory. An exhaustive search was used to fill in the important gap when w = 8, which is highly applicable to real-world systems, since it is a power of 2. This paper extends that approach to address the next theoretical hole at w = 9 by expanding upon the techniques used for w = 8 and adding customizations to allow for parallel processing.