Abstract: Quantum error-correcting codes play an important role in not only quantum communication but also quantum computation. Many good quantum error-correcting codes have been constructed by using classical linear codes, for example, Hamming codes, BCH codes, RS codes and Reed-Muller codes. A new method to obtain quantum codes and asymmetric quantum codes is presented. Based on line graph of the n-cube, infinite families of new quantum codes and asymmetric quantum codes are presented. Moreover, if the length of asymmetric quantum codes is large, the asymmetric quantum codes are able to correct quantum errors with great asymmetry.

Key words: quantum error-correcting codes, asymmetric quantum error-correcting codes, n-cube, linear code

摘要： 量子纠错码在量子通信和量子计算中起着非常重要的作用，之前的量子纠错码的构造大部分都是利用经典的纠错码来构造得到，如Hamming码，BCH码，RS码，Reed-Muller码等各种经典纠错码。目前，很少有人利用图生成的线性码方法来构造量子纠错码，提出了一个新的构造量子纠错码和非对称量子纠错码的方法，即利用[n]立方图的线图生成的二元线性码来构造量子纠错码和非对称量子纠错码，得到了一类新的量子纠错码和非对称量子纠错码，并且，当码字的长度较大时，对所构造的非对称量子纠错码，在非对称信道上有更大的纠错能力。

关键词: 量子纠错码, 非对称量子纠错码, 立方图, 线性码