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In this paper, we study a family of constacyclic BCH codes over$\mathbb{F}_{q^2}$ of length $n=\frac{q^{2m}-1}{q+1}$, where $q$ is a primepower, and $m\geq2$ an even integer. The maximum design distance ofnarrow-sense Hermitian dual-containing constacyclic BCH codes of length $n$ isdetermined. Furthermore, the exact dimension of the constacyclic BCH codes withgiven design distance is computed. As a consequence, we are able to derive theparameters of quantum codes as a function of their design parameters of theassociated constacyclic BCH codes. This improves the result by Yuan et al. (DesCodes Cryptogr 85(1): 179-190, 2017), showing that with the same lengths,except for three trivial cases ($q=2,3,4$), our resultant quantum codes canalways yield strict dimension or minimum distance gains than the ones obtainedby Yuan et al.. Moreover, fixing length $n=\frac{q^{2m}-1}{q+1}$, someconstructed quantum codes have better parameters or are beneficial complementscompared with some known results (Aly et al., IEEE Trans Inf Theory 53(3):1183-1188, 2007, Li et al., Quantum Inf Process 18(5): 127, 2019, Wang et al.,Quantum Inf Process 18(8): 323, 2019, Song et al., Quantum Inf Process 17(10):1-24, 2018.).

Hermitian dual-containing constacyclic BCH codes and related quantum codes of length $\frac{q^{2m}-1}{q+1}$