On the Constructions of Entanglement-Assisted Quantum MDS Codes

Entanglement-assisted quantum error-correcting codes, which is a generalization of quantum error-correcting codes, could be derived from any classical codes by utilizing pre-shared entangled states between the sender and the receiver. In this paper, we construct some entanglement-assisted quantum maximum-distance-separable (EAQMDS) codes from constacyclic codes and cyclic codes by exploiting less pre-shared entangled states, respectively. Most of these codes are new in the sense that their parameters are not covered by the codes available in the literature. In particular, we extend the results in Tian et al. (Int. J. Theor. Phys. 60, 1843-1857, 2021) to more general case.