Generalized cube networks are limited to single-fault tolerance with respect to permutation connections. The vector space approach presented here yields many fault-tolerance schemes that can tolerate two and three faults. In each scheme, redundant switches and links are added to networks and interconnected in certain ways. These redundancies are represented by a matrix called the redundancy matrix. A fault-free network without redundancy is represented by an identity matrix. As faulty switches and links are discovered, the remaining switches and links are remapped to establish an intact network. The remapping is analogous to converting an invertible redundancy matrix back to an identity matrix.>