Optimal fault-tolerant routing is imperative for large hypercube systems in the existence of large number of faulty links or nodes. This paper first defines hypercube network with a large number of faulty nodes and/or links to be generalized hypercube and illustrates that many non-hypercube systems can be transformed to Generalized Hypercube systems. It then proposes node path vector (NPV) to capture the complete optimal and sub-optimal routing information for a generalized hypercube system. To reduce the computation iterations in solving NPV, it also introduces the concept of relay node technique. Based on NPV and relay node technique, this paper further proposes optimal fault-tolerant routing scheme (OFTRS) to derive shortest path for any communication pair in a generalized hypercube system. With an example of large number of faulty nodes or faulty links, it is illustrated that the previous algorithm could omit up to 60% routing paths, while this approach achieves all optimal and sub-optimal routing paths. Compared to previous work, OFTRS has a significant improvement in obtaining routing information for optimal and sub-optimal, i.e. no matter how many faulty nodes or links exist, it is guaranteed to route through the optimal or sub-optimal path as long as a path between the source-destination pair exists. In addition, the proposed scheme is distributed and relying only on non-faulty neighboring nodes since it only requires the information of non-faulty neighbor nodes in computing NPV, thus it has high applicability, especially when some non-hypercube systems can be transformed into Generalized Hypercube systems.