We give a new construction of binary quantum codes that enables the generation of a CSS-T code from any given CSS code. Using this construction, we prove the existence of asymptotically good binary CSS-T codes, resolving a previously open problem in the literature. Furthermore, we demonstrate that the same result holds for binary quantum low-density parity check CSS-T codes, and establish the existence of asymptotically good CSS codes that support any given $Z$ rotation transversally. Finally, we analyze the structure of the logical operators corresponding to certain non-Clifford gates supported by the quantum codes obtained from our construction.

翻译：我们提出了一种新的二进制量子码构造方法，能够从任意给定的CSS码生成CSS-T码。利用该构造，我们证明了渐近优二进制CSS-T码的存在性，解决了文献中先前悬而未决的问题。此外，我们证明了相同结论对二进制量子低密度奇偶校验CSS-T码同样成立，并建立了支持任意给定$Z$旋转横向操作的渐近优CSS码的存在性。最后，我们分析了通过该构造获得的量子码所支持的特定非克利福德门对应的逻辑算子结构。