Entanglement-assisted quantum error correcting codes (EAQECCs) play a significant role in protecting quantum information from decoherence and quantum noise. Recently, constructing entanglement-assisted quantum maximum distance separable (EAQMDS) codes with flexible parameters has received much attention. In this work, four families of EAQMDS codes with a more general length are presented. And the method of selecting defining set is different from others. Compared with all the previously known results, the EAQMDS codes we constructed have larger minimum distance. All of these EAQMDS codes are new in the sense that their parameters are not covered by the quantum codes available in the literature.

中文翻译：

---

循环码和一些新的纠缠辅助量子 MDS 码

纠缠辅助量子纠错码 (EAQECC) 在保护量子信息免于退相干和量子噪声方面发挥着重要作用。最近，构建具有灵活参数的纠缠辅助量子最大距离可分（EAQMDS）码受到了广泛关注。在这项工作中，提出了四个具有更一般长度的 EAQMDS 代码系列。并且选择定义集的方法与其他方法不同。与之前已知的所有结果相比，我们构建的 EAQMDS 代码具有更大的最小距离。所有这些 EAQMDS 代码都是新的，因为它们的参数没有被文献中可用的量子代码覆盖。