Abstract: Quantum error correction plays a crucial role in quantum information theory. Schlingemann and Werner presented a new way to construct quantum stabilizer codes by finding certain graphs（or matrices）with specific properties, and they constructed several new nonbinary quantum codes by the way, in particular, they gave a new proof on existence of quantum codes[[[5,1,3]]p][(p≥3)]. The way can be generalized the construction of symmetric quantum codes to the asymmetric case. Using this method, the existence of asymmetric graph quantum MDS codes with parameters[[[5,1,4/2]]p] and [[[7,1,6/2]]p]is showed separately for all primes[p>5]and[p>7]by graph machinery.

Key words: asymmetric quantum codes, quantum MDS codes, graph construction

摘要： 量子纠错编码技术在量子信息理论中一直以来有着重要的地位，在量子纠错编码方案中，Schingemann和Werner两人提出了通过构造具有某些性质的图（矩阵）来构造非二元量子码的方法，他们利用这种图论方法构造出很多好的量子码，特别给出量子码[[[5,1,3]]p][(p≥3)]存在性的一个新证明。此方法可从对称量子码推广至非对称量子码的构造，利用推广方法证明了非对称图量子MDS码[[[5,1,4/2]]p]，[(p>5)]和[[[7,1,6/2]]p][(p>7)]的存在性。

关键词: 非对称量子码, 量子MDS码, 图构造