Constacyclic BCH codes, as a generalization of BCH codes, have been widely used in the construction of quantum codes. In this paper, we mainly study narrow-sense Hermitian dual-containing constacyclic BCH codes over \(\mathbb {F}_{q^2}\) of new length \(n=\frac{q^{2m}-1}{a(q+1)}\) , where q is a prime power, \(m \ge 3\) is an odd integer and \(a \ne 1\) is a divisor of \(q-1\) , as well as of length \(n=\frac{2(q^m+1)}{q+1}\) , where q is an odd prime power and \(m \ge 3\) is odd. Firstly, we present some necessary and sufficient conditions for these constacyclic BCH codes to be Hermitian dual-containing. Secondly, the explicit dimensions of these constacyclic BCH codes are completely determined. Furthermore, some quantum codes with new parameters are constructed by these Hermitian dual-containing constacyclic BCH codes.
