Two Families of Entanglement-Assisted Quantum Codes Constructed from Cyclic Codes

Entanglement-assisted quantum error-correcting (EAQEC) codes are a significant extension of quantum error-correcting codes. It has been found that an EAQEC code can be constructed by an arbitrary classical linear code if the encoder and the decoder share the entangled state c in advance. In this paper, we construct two families of q-ary entanglement-assisted quantum maximum-distance-separable (EAQMDS) codes. This construction produces new EAQMDS codes with variable parameters with respect to the minimum distance d and the number c of maximally entangled states. Moreover, the resulting EAQMDS codes have minimum distance not less than q.