A New Class of MDS Erasure Codes Based on Graphs
  Maximum distance separable (MDS) array codes are XOR-based optimal erasure codes that are particularly suitable for use in disk arrays. This paper develops an innovative method to build MDS array codes from an elegant class of nested graphs, termed \textit{complete-graph-of-rings (CGR)}. We discuss a systematic and concrete way to transfer these graphs to array codes, unveil an interesting relation between the proposed map and the renowned perfect 1-factorization, and show that the proposed CGR codes subsume B-codes as their "contracted" codes. These new codes, termed \textit{CGR codes}, and their dual codes are simple to describe, and require minimal encoding and decoding complexity. 
Nattakan Puttarak, Phisan Kaewprapha, Boon Chong Ng, Jing (Tiffany) Li
cs.IT math.IT