New asymmetric quantum codes over $$F_{q}$$ 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 $$n=q^{m}-1$$n=qm-1 over $$F_{q}$$Fq, where $$q\ge 5$$qź5 is a prime power. The second one is the asymmetric quantum codes with length $$n=3^{m}-1$$n=3m-1. These asymmetric quantum codes are derived from the CSS construction and pairs of nested BCH codes. Moreover, let the defining set $$T_{1}=T_{2}^{-q}$$T1=T2-q, then the real Z-distance of our asymmetric quantum codes are much larger than $$\delta _\mathrm{max}+1$$źmax+1, where $$\delta _\mathrm{max}$$źmax 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.