I consider the theory of quantum error correcting code (QECC) where each quantum particle has more than two possible eigenstates. In this higher spin system, I report an explicit QECC that is related to the symmetry group ${ \Bbb Z}_2^{ \otimes (N-1)} \otimes S_N$. This QECC, which generalizes Shor's simple majority vote code, is able to correct errors arising from exactly one quantum particle. I also provide a simple encoding algorithm.
Categories: quant-ph