A small overhead storage room MDS code with zigzag—Decodable property for distributed storage

A code that has properties binary field operation, MDS, zigzag decodable, requiring symmetric storage room, and requiring small additional storage overhead, is designed. To ensure the above properties, the key technique we utilize is cyclic shift plus permutation misalignment. Though the code is designed specially for (4, 8) MDS code in this stage, it sheds light on further generalization to arbitrary MDS code.