Subsystem codes over nice nearrings

Subsystem codes are quantum error correcting schemes unifying stabilizer codes, decoherence free subspaces and noiseless subsystems. Subsystem codes were most commonly based on the generalized Pauli basis with dimensions of a power of prime. Recently, a class of nice error bases indexed by a nearring were introduced by the second author. We give a construction of subsystem codes over nice nearrings. Furthermore, we show that free subsystem codes over a finite chain ring cannot perform better than those over a finite field.