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Entanglement-assisted quantum error-correcting codes expand the usual paradigm of quantum error correction by allowing two parties to make use of pre-shared entanglement. This entanglement can increase either the rate of communication or the number of correctable errors. By employing generalized Reed–Solomon codes, we construct several classes of entanglement-assisted quantum maximum distance separable (EAQMDS) codes in this paper. Consequently, the results show that many of these EAQMDS codes have much larger minimum distance than ones available in the literature. Meanwhile, some of these EAQMDS codes are new in the sense that the parameters of these codes are not covered by the previously known ones, whose required number of maximally entangled states is more flexible. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]