A class of constacyclic BCH codes of length \(n=\frac{q^{2m}-1}{2\left( q^2-1\right) }\) and related quantum codes

In this paper, a class of narrow-sense constacyclic BCH codes over \(\mathbb {F}_{q^2}\) ${\mathbb{F}}_{q^2}$ with length \(n=\frac{q^{2m}-1}{2\left( q^2-1\right) }\) $n=\frac{q^{2m}-1}{2\left(q^2,-,1\right)}$ is studied, where \(q\ge 3\) $q\ge 3$ is an odd prime power and \(m\ge 2\) $m\ge 2$ is even. The maximum designed distance such that narrow-sense constacyclic BCH codes over \(\mathbb {F}_{q^2}\) ${\mathbb{F}}_{q^2}$ with length n containing their Hermitian dual codes is determined. We obtain some new quantum codes by using such narrow-sense constacyclic BCH codes. Our constructions not only have larger designed distance but also have better parameters than the ones in the literature.