With the number of nodes increasing in scale, the requirements of storage space enlarge sharply in distributed storage systems. Failure-tolerance schemes such as Reed–Solomon codes (RS codes in short) and Cauchy Reed–Solomon codes (CRS codes in short) are used to save storage space. However, these failure-tolerance schemes severely degrade the system performance. In this paper, we propose optimal RS codes (OptRS codes in short) based on RS codes and CRS codes that can offer better performance for encoding and decoding as well as maximizing the utilization of storage space. OptRS codes can speed up the matrix computation which is regarded as the most important factor to impact the efficiency of coding by transferring the matrix computation from the Galois field mapping to the XOR operation. OptRS codes employ an algorithm called row elimination scheme (RE scheme in short), which can eliminate the same XOR operation to minimize the number of XOR operations. We analyze optimal matrices (OM in short) in theory, which prove the optimal performance of OptRS codes over the Galois field. Our method is implemented on the top of the distributed storage system, and code parameters were carefully chosen. The test result shows that OptRS codes can improve the performance in different data block numbers, parity block numbers, block size, normal reading, and degraded reading, compared with RS codes and CRS codes.
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