An Exponential Length Universal Hamming Code Correct Algorithm

Any length of 2^J bit Boolean data to have the correct code which has the uniform structure and formula is provided. The algorithm is derived from the concept of the linear group code, based on the deducing of generator matrix and the corresponding parity check matrix, we conclude the algorithm can correct one bit data and identify two bit data. Then based on the analysis of the position of the data in the formula, we get the information of the position of the error data. And we get the uniform formula. The experiment validates the correctness of the algorithm. The algorithm is adaptive to the high speed data storage and transfer.