The exact-repair regeneration codes for distributed storage system are studied in this work. A novel coding scheme is proposed for code construction for any (n, k, d = k) system, and it is shown to be optimal. In particular, the optimum tradeoff of exact-repair regeneration system is fully characterized for any system with d = k. The new construction is based on fundamental properties of matrix determinant, thus the code is called determinant code. It is devised for the entire range of (α, β) on the optimum tradeoff.