Patent ID: 8412762

Claim:
A computer-implemented error-correcting method used in data transmission and decoding, analyzing data received by a receiver, comprising: providing, in a storage device, a first equation for processing of the data to accordingly generate a first sum, wherein the first equation comprises a plurality of XOR operations, according to the first equation, each bit of the data is multiplied by an exponentiation α n , wherein α is a parameter, and n relates to a position of a corresponding bit, and a multiplication result corresponding to the said each bit is processed by an XOR operation, a result of the XOR operation of the first equation is 0 when there is no erroneous bit in the data; providing, in the storage device, a second equation for processing of the data to accordingly generate a second sum; dividing, by a processor, the second sum with the first sum, and identifying a position of an erroneous bit in the data according to a result obtained from the division operation.