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The erasure codes are widely used in the distributed storage with low redundancy compared to the replication method. However, the current research studies about the erasure codes mainly focus on the encoding methods, while there are few studies on the decoding methods. In this paper, a novel erasure decoding method is proposed; it is a general decoding method and can be used both over the multivariate finite field and the binary finite field. The decoding of the failures can be realized based on the transforming process of the decoding transformation matrix, and it is convenient to avoid the overburdened visiting problem by tiny modification of the method. The correctness of the method is proved by the theoretical analysis; the experiments about the comparison with the traditional methods show that the proposed method has better decoding efficiency and lower reconstruction bandwidth.

A Novel Decoding Method for the Erasure Codes