We present a family of quantum stabilizer codes using the structure of duadic constacyclic codes over $\mathbb{F}_4$. Within this family, quantum codes can possess varying dimensions, and their minimum distances are lower bounded by a square root bound. For each fixed dimension, this allows us to construct an infinite sequence of binary quantum codes with a growing minimum distance. Additionally, we prove that this family of quantum codes includes an infinite subclass of degenerate codes. We also introduce a technique for extending splittings of duadic constacyclic codes, providing new insights into the minimum distance and minimum odd-like weight of specific duadic constacyclic codes. Finally, we provide numerical examples of some quantum codes with short lengths within this family.

翻译：本文利用$\mathbb{F}_4$上对偶常循环码的结构，提出了一族量子稳定子码。在该族中，量子码可具有不同的维数，其最小距离受平方根下界约束。对于每个固定维数，这使我们能够构造最小距离不断增长的无限序列二进制量子码。此外，我们证明该族量子码包含无限子类的退化码。我们还提出了一种扩展对偶常循环码分裂的技术，为特定对偶常循环码的最小距离及最小奇类重量提供了新的见解。最后，我们给出了该族中若干短长度量子码的数值算例。