We present a family of non-CSS 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 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 demonstrate that this quantum family includes an infinite subclass of degenerate codes with the mentioned properties. 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 establish that many best-known quantum codes belong to this family and provide numerical examples of quantum codes with short lengths within this family.

翻译：我们提出了一族基于$\mathbb{F}_4$上对偶循环码结构的非CSS量子稳定子码。在该族中，量子码可具有不同维度，其最小距离受平方根界约束。对于每个固定维度，此构造允许我们生成具有递增最小距离的无限序列二元量子码。此外，我们证明该量子族包含具有上述性质的无限子类退化码。我们还引入了一种扩展对偶循环码分裂的技术，为特定对偶循环码的最小距离和最小奇权值提供了新见解。最后，我们证实许多已知最优量子码属于该族，并给出了该族内短码长的数值示例。