  Entanglement-assisted quantum error-correcting codes (EAQECCs) make use of
preexisting entanglement between the sender and receiver to boost the rate of
transmission. It is possible to construct an EAQECC from any classical linear
code, unlike standard quantum error-correcting codes, which can only be
constructed from dual-containing codes. However, the parameter of ebits $c$ is
usually calculated by computer search. In this paper, we construct four classes
of MDS entanglement-assisted quantum error-correcting codes (MDS EAQECCs) based
on $k$-Galois LCD MDS codes for some certain code lengths, where the parameter
of ebits $c$ can be easily generated algebraically and not by computational
search. Moreover, the constructed four classes of EAQECCs are also
maximal-entanglement EAQECCs.
