Abstract: Compared with cross-cloud data center replication, cross-cloud data center erasure code is more reliable and space-efficiency. However, as existing cross-cloud data center erasure codes cannot achieve low cross-cloud data center repair traffic, high encoding parameters adaptability, and high erasure code construction efficiency at the same time, they are rarely used in production. This paper proposes a fast construction method of the erasure code with small cross-cloud data center repair traffic, called FMEL, which can obtain the erasure code with small cross-cloud data center repair traffic quickly under different encoding parameters. Specifically, FMEL converts erasure code repair group distribution schemes and the corresponding encoding parameters into fixed-length feature vectors, and verifies erasure code repair group distribution schemes quickly by classifying corresponding feature vectors with an support vector machine—a feature vector is positive indicates that the corresponding erasure code repair group distribution scheme passes the verification. Then, FMEL uses a parallel search algorithm to pick the erasure code repair group distribution scheme with the smallest cross-cloud data center repair traffic from all distribution schemes passing the verification and converts it into the generator matrix of the erasure code with small cross-cloud data center repair traffic. Experiments in a cross-cloud data center environment show that FMEL can construct the optimal code that can achieve the lower bound of cross-cloud data center repair traffic under most encoding parameters. Meanwhile, FMEL's erasure code construction time is 89% less than the existing work's optimal code construction time. Meanwhile, compared with several popular erasure codes, the erasure code constructed by FMEL can reduce the cross-cloud data center repair traffic by 42.9%—56.0%.