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A new class of Binary Maximum Distance Separable (MDS) array codes which are based on circular permutation matrices are introduced in this paper. These array codes are used for tolerating multiple (greater than or equal to 4) disk failures in Redundant Arrays of Inexpensive Disks (RAID) architecture. The size of the information part is m \times n, where n is the number of information disks and (m+1) is a prime integer; the size of the parity-check part is m \times r, the minimum distance is r+1, and the number of parity-check disks is r. In practical applications, m can be very large and n ranges from 20 to 50. The code rate is R = {\frac{n}{n+r}}. These codes can be used for tolerating up to r disk failures, with very fast encoding and decoding. The complexities of encoding and decoding algorithms are O(rmn) and O(m^3r^4), respectively. When r=4, there need to be 9mn XOR operations for encoding and (9n+95)(m+1) XOR operations for decoding.
Index Terms- Rabin codes, MDS array codes, RAID, multiple disk failures.

G. Feng, F. Bao, J. Shen and R. H. Deng, "New Efficient MDS Array Codes for RAID Part II: Rabin-Like Codes for Tolerating Multiple (greater than or equal to 4) Disk Failures," in IEEE Transactions on Computers, vol. 54, no. , pp. 1473-1483, 2005.
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