一种指数字长的通用汉明码纠错算法

An Exponential Length Universal Hamming Code Correct Algorithm

提出一种对于任意2J bit字长的布尔数据,能够根据统一的结构、统一的公式,对有效数据进行纠错编码.该算法从线性分组码的基本概念出发,通过对生成矩阵和一致校验矩阵的推导,得出了该算法能够纠错一位数据,检错两位数据的结论,并通过对有效数据的码位分析,得出错误位的信息,并因此得出该纠错算法的统一的公式.并通过实验验证了该算法的正确性.适用于高速数据的存储和传输.

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.