Abstract
Entanglement-assisted quantum error-correcting codes (abbreviate to EAQECCs) expand the usual paradigm of quantum error correction by allowing two parties to make use of pre-shared entanglement. It is well-known that we can construct an EAQECC from arbitrary classical linear code. In this paper, we construct several classes of entanglement-assisted quantum MDS (EAQMDS) codes by utilizing generalized Reed-Solomon (GRS) codes. The main contribution of the paper is extend the code length of EAQMDS in the literature (Guo et al. 2019). Consequently, the results show that almost all of these EAQMDS codes are new in the sense that the parameters of these codes are not covered by the previously known ones.
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