STAR+ Codes: Triple-Fault-Tolerant Codes with Asymptotically Optimal Updates and Efficient Encoding/Decoding

STAR codes are well-known binary Maximum Distance Separable (MDS) array codes with triple fault tolerance and low encoding/decoding complexity, yet the update complexity of STAR codes is sub-optimal. We propose STAR+ codes, which extend STAR codes to achieve asymptotically optimal update complexity. We show that STAR+ codes are the generalized version of STAR codes with triple fault tolerance, and additionally have strictly less complexity in encoding, decoding, and updates than STAR codes for most parameters.