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 apply 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码是近年来提出的可容忍横向门的量子纠错码。CSS-T码依赖于CSS-T对，即一对二元码(C₁, C₂)满足C₁包含C₂、C₂为偶码，且C₁对偶码关于C₂每个码字支撑集的缩短码为自对偶码。本文给出了保证二元码对(C₁, C₂)为CSS-T对的新条件。我们定义了CSS-T对的偏序集，并确定了该偏序集的极大元和极小元。提出了非简并CSS-T码的传播规则。将主要结果应用于Reed-Muller码、循环码和扩展循环码。利用定义分圆陪集刻画了循环码的CSS-T对。通过构造循环码和扩展循环码，获得了参数优于现有文献的量子码。