It is very difficult to deal with the problem of error correction in random network coding, especially when the number of errors is more than the min-cut of the network. We combine a small field with rank-metric codes to solve this problem in this paper. With a small finite field, original errors are compressed to propagated errors, and their number is smaller than the min-cut. Rank-metric codes are introduced to correct the propagated errors, while the minimum rank distance of the rank-metric code is hardly influenced by the small field. It is the first time to correct errors more than the min-cut in network coding with our method using a small field. This new error-correcting algorithm is very useful for the environment such as a wireless sensor network where network coding can be applied.

处理随机网络编码中的纠错问题非常困难，尤其是当错误数量大于网络的最小割数时。在本文中，我们将小字段与等级度量代码结合起来以解决此问题。在有限字段的情况下，原始错误被压缩为传播错误，并且其数目小于最小割限。引入了秩度量码以校正传播的误差，而秩度量码的最小秩距离几乎不受小场的影响。这是我们第一次使用小范围的方法来纠正错误，而不是最小化网络编码中的错误。这种新的纠错算法对于可以应用网络编码的环境（例如无线传感器网络）非常有用。