纠单错和检邻接错的(12,8)系统码

A Systematic (12,8)Code for Correcting Single Errors and Detecting Adjacent Errors

本文给出了一个(12,8)系统码的奇偶校验矩阵,该系统码可以用来纠所有的单错和检测在任意三个半字节中9个双邻接错其中的8个,而且还证明了不存在这样一种(12,8)系统二进码既可以用来纠所有的单错又可以检出在三个半字节当中的9个双邻接错。

A Parity check matrix is given for a systematic (12, 8) binary code which corrects all single errors and detects eight of the nine double adjacent errors within any of the three nibbles. Furthermore, it is shown that there can not exist a (12, 8) systematic binary code that corrects all single errors and detects all nine of the double adjacent errors within the three nibbles.