In this paper, we focus on the problem of computing the set of diagonal transversal gates fixing a CSS code. We determine the logical actions of the gates as well as the groups of transversal gates that induce non-trivial logical gates and logical identities. We explicitly declare the set of equations defining the groups, a key advantage and differentiator of our approach. We compute the complete set of transversal stabilizers and transversal gates for any CSS code arising from monomial codes, a family that includes decreasing monomial codes and polar codes. As a consequence, we recover and extend some results in the literature on CSS-T codes, triorthogonal codes, and divisible codes.

翻译：本文聚焦于计算固定CSS码的对角横向门集合问题。我们确定了这些门的逻辑作用，以及诱导非平凡逻辑门和逻辑恒等式的横向门群。我们明确给出了定义这些群的方程组，这是本方法的关键优势与特色。针对任意由单项式码（包含递减单项式码与极化码的码族）生成的CSS码，我们计算了其完整的横向稳定子集与横向门集合。由此，我们恢复并扩展了文献中关于CSS-T码、三重正交码与可除码的若干结果。