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Entanglement-assisted quantum error-correcting codes (EAQECCs) make use ofpreexisting entanglement between the sender and receiver to boost the rate oftransmission. It is possible to construct an EAQECC from any classical linearcode, unlike standard quantum error-correcting codes, which can only beconstructed from dual-containing codes. However, the parameter of ebits $c$ isusually calculated by computer search. In this paper, we construct four classesof MDS entanglement-assisted quantum error-correcting codes (MDS EAQECCs) basedon $k$-Galois LCD MDS codes for some certain code lengths, where the parameterof ebits $c$ can be easily generated algebraically and not by computationalsearch. Moreover, the constructed four classes of EAQECCs are alsomaximal-entanglement EAQECCs.

Entanglement-assisted quantum codes from Galois LCD codes