  Recently, entanglement-assisted quantum error correcting codes (EAQECCs) have
been constructed by cyclic codes and negacyclic codes. In this paper, by
analyzing the cyclotomic cosets in the defining set of constacyclic codes, we
constructed three classes of new EAQECCs which satisfy the
entanglement-assisted quantum Singleton bound. Besides, three classes of
EAQECCs with maximal entanglement from constacyclic codes are constructed in
the meanwhile.
