The theory of quantum error-correcting codes has been extended to asymmetric quantum channels-qubit-flip and phase-shift errors may have equal or different probabilities. Previous work in constructing quantum error-correcting codes has focused on code constructions for symmetric quantum channels. Recently, Galindo et al. introduced the concept of asymmetric entanglement-assisted quantum error-correcting (AEAQEC) code, and gave a Gilbert–Varshamov bound for AEAQEC codes. Then they present the explicit computation of the parameters of AEAQEC codes coming from BCH codes. In this paper, we first establish a bound for pure AEAQEC codes similar to the quantum Singleton bound, and introduce the definition of pure AEAQEC MDS codes. Then we construct three new families of AQEAEC codes by means of Vandermonde matrices, extended GRS codes and cyclic codes. The AEQAEC codes here have better parameters than the ones available in the literature.

量子纠错码的理论已扩展到非对称量子通道-比特翻转和相移误差可能具有相同或不同的概率。构造量子纠错码的先前工作集中在对称量子信道的码构造上。最近，Galindo等人。引入了非对称纠缠辅助量子纠错（AEAQEC）代码的概念，并给出了针对AEAQEC代码的吉尔伯特-瓦尔沙莫夫界线。然后，他们给出了来自BCH码的AEAQEC码参数的显式计算。在本文中，我们首先为纯AEAQEC码建立了一个与量子单例绑定相似的界，并介绍了纯AEAQEC MDS码的定义。然后，我们通过范德蒙矩阵，扩展的GRS码和循环码构造了三个新的AQEAEC码族。