  I construct a quantum error correction code (QECC) in higher spin systems
using the idea of multiplicative group character. Each $N$ state quantum
particle is encoded as five $N$ state quantum registers. By doing so, this code
can correct any quantum error arising from any one of the five quantum
registers. This code generalizes the well-known five qubit perfect code in
spin-1/2 systems and is shown to be optimal for higher spin systems. I also
report a simple algorithm for encoding. The importance of multiplicative group
character in constructing QECCs will be addressed.
