Generalized X-code: An efficient RAID-6 code for arbitrary size of disk array

Many RAID-6 codes have been proposed in the literature, but each has its limitations. Horizontal code has the ability to adapt to the arbitrary size of a disk array but its high computational complexity is a major shortcoming. In contrast, the computational complexity of vertical code (e.g. X-code) often achieves the theoretical optimality, but vertical code is limited to using a prime number as the size of the disk array In this article, we propose a novel efficient RAID-6 code for arbitrary size of disk array: generalized X-code. We move the redundant elements along their calculation diagonals in X-code onto two specific disks and change two data elements into redundant elements in order to realize our new code. The generalized X-code achieves optimal encoding and updating complexity and low decoding complexity; in addition, it has the ability to adapt to arbitrary size of disk array. Furthermore, we also provide a method for generalizing horizontal code to achieve optimal encoding and updating complexity while keeping the code's original ability to adapt to arbitrary size of disk array.