CSS-T codes were recently introduced as quantum error-correcting codes that respect a transversal gate. A CSS-T code depends on a CSS-T pair, which is a pair of binary codes $(C_1, C_2)$ such that $C_1$ contains $C_2$, $C_2$ is even, and the shortening of the dual of $C_1$ with respect to the support of each codeword of $C_2$ is self-dual. In this paper, we give new conditions to guarantee that a pair of binary codes $(C_1, C_2)$ is a CSS-T pair. We define the poset of CSS-T pairs and determine the minimal and maximal elements of the poset. We provide a propagation rule for nondegenerate CSS-T codes. We applied some main results to Reed-Muller, cyclic, and extended cyclic codes. We characterize CSS-T pairs of cyclic codes in terms of the defining cyclotomic cosets. We find cyclic and extended cyclic codes to obtain quantum codes with better parameters than those in the literature.

翻译：CSS-T码是近年来被引入的一类尊重横向逻辑门的量子纠错码。CSS-T码依赖于一个CSS-T对，即满足以下条件的二进制码对$(C_1, C_2)$：$C_1$包含$C_2$，$C_2$为偶重量码，且$C_1$的对偶码在$C_2$每个码字支撑集上的缩短化为自对偶码。本文给出了保证二进制码对$(C_1, C_2)$为CSS-T对的新条件，定义了CSS-T对的偏序集，并确定了该偏序集的极小元和极大元。我们为非退化CSS-T码提供了传播规则，并将主要结果应用于Reed-Muller码、循环码及扩展循环码。通过定义分圆陪集刻画了循环码的CSS-T对，发现了比现有文献参数更优的量子码对应的循环码与扩展循环码。