Construction of Linear Codes over Rings Zm Correcting Double ±1 or ±2 Errors

In this paper a construction of double ±1 and ±2 errors correcting linear optimal and quasi-optimal codes over rings Z5, Z7 and Z9 is presented with the limitation that both errors have the same amplitude in absolute value.

Quantum codes over rings

This paper considers the construction of quantum error correcting codes from linear codes over finite commutative Frobenius rings. We extend the Calderbank–Shor–Steane (CSS) construction to these rings. Further, quantum codes are extended to matrix product codes. Quantum codes over 𝔽pk are also obtained from linear codes over rings using the generalized Gray map.