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 inform...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.展开更多
The problem of reconstruction of a binary image in the field of discrete tomography is a classic instance of seeking solution applying mathematical techniques. Here two such binary image reconstruction problems are co...The problem of reconstruction of a binary image in the field of discrete tomography is a classic instance of seeking solution applying mathematical techniques. Here two such binary image reconstruction problems are considered given some numerical information on the image. Algorithms are developed for solving these problems and correctness of the algorithms are discussed.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.61501064Sichuan Provincial Science and Technology Project under Grant No.2016GZ0122
文摘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.
基金a FRGS grant No.203/PKOMP/6711267an ERGS Grant No.203/PKOMP/6730075 of the Ministry of Higher Education(MoH E),Malaysia
文摘The problem of reconstruction of a binary image in the field of discrete tomography is a classic instance of seeking solution applying mathematical techniques. Here two such binary image reconstruction problems are considered given some numerical information on the image. Algorithms are developed for solving these problems and correctness of the algorithms are discussed.
