Some construction of entanglement-assisted quantum MDS codes

Entanglement-assisted quantum error-correcting codes expand the usual paradigm of quantum error correction by allowing two parties to make use of pre-shared entanglement. This entanglement can increase either the rate of communication or the number of correctable errors. By employing generalized Reed-Solomon codes, we construct several classes of entanglement-assisted quantum maximum distance separable (EAQMDS) codes in this paper. Consequently, the results show that many of these EAQMDS codes have much larger minimum distance than ones available in the literature. Meanwhile, some of these EAQMDS codes are new in the sense that the parameters of these codes are not covered by the previously known ones, whose required number of maximally entangled states is more flexible.