In this study, we investigate the construction of quantum CSS duadic codes with dimensions greater than one. We introduce a method for extending smaller splittings of quantum duadic codes to create larger, potentially degenerate quantum duadic codes. Furthermore, we present a technique for computing or bounding the minimum distances of quantum codes constructed through this approach. Additionally, we introduce quantum CSS triadic codes, a family of quantum codes with a rate of at least $\frac{1}{3}$.

翻译：本研究探讨了维度大于一的量子CSS对偶码的构造方法。我们提出了一种通过扩展较小分裂的量子对偶码来构建更大、可能退化的量子对偶码的技术。进一步，我们给出了计算或界定通过此方法构造的量子码最小距离的方法。此外，我们引入了量子CSS三元码，这是一类码率至少为$\frac{1}{3}$的量子码族。