A novel class of exact-repair regenerating codes is introduced for a distributed storage system with arbitrary parameters (n, k, d). The proposed construction is based on the optimum determinant codes for (n, k=d, d) systems. This construction yields an achievable trade-off between the storage and the repair bandwidth, consisting of k corner points, which meets the optimum trade-off at the MBR and MSR points, and improves all the previously known bounds for interior points. The sub-packetization level of the proposed code only depends on k and d, but not number of nodes n. Further, the required field size for the proposed code is Θ(n). We conjecture that the proposed codes can universally achieve the optimum trade-off.