New asymmetric quantum codes over $F_{q}$

Abstract

Two families of new asymmetric quantum codes are constructed in this paper. The first family is the asymmetric quantum codes with length $n=q^{m}-1$ over $F_{q}$, where $q\ge 5$ is a prime power. The second one is the asymmetric quantum codes with length $n=3^{m}-1$. These asymmetric quantum codes are derived from the CSS construction and pairs of nested BCH codes. Moreover, let the defining set $T_{1}=T_{2}^{-q}$, then the real Z-distance of our asymmetric quantum codes are much larger than $\delta _\mathrm{max}+1$, where $\delta _\mathrm{max}$ is the maximal designed distance of dual-containing narrow-sense BCH code, and the parameters presented here have better than the ones available in the literature.