Correcting quantum errors in higher spin systems

I consider the theory of the 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 Z₂^(N-1){}SN. This QECC, which generalizes Shor's simple majority vote code [Phys. Rev. A 52, 2493 (1995)], is able to correct errors arising from exactly one quantum particle. I also provide a simple encoding algorithm.