In the process of encoding and decoding,erasure codes over binary fields,which just need AND operations and XOR operations and therefore have a high computational efficiency,are widely used in various fields of information technology.A matrix decoding method is proposed in this paper.The method is a universal data reconstruction scheme for erasure codes over binary fields.Besides a pre-judgment that whether errors can be recovered,the method can rebuild sectors of loss data on a fault-tolerant storage system constructed by erasure codes for disk errors.Data reconstruction process of the new method has simple and clear steps,so it is beneficial for implementation of computer codes.And more,it can be applied to other non-binary fields easily,so it is expected that the method has an extensive application in the future.
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