We investigate CSS and CSS-T quantum error-correcting codes from the point of view of their existence, rarity, and performance. We give a lower bound on the number of pairs of linear codes that give rise to a CSS code with good correction capability, showing that such pairs are easy to produce with a randomized construction. We then prove that CSS-T codes exhibit the opposite behaviour, showing also that, under very natural assumptions, their rate and relative distance cannot be simultaneously large. This partially answers an open question on the feasible parameters of CSS-T codes. We conclude with a simple construction of CSS-T codes from Hermitian curves. The paper also offers a concise introduction to CSS and CSS-T codes from the point of view of classical coding theory.

翻译：我们从存在性、稀有性及性能角度研究CSS与CSS-T量子纠错码。我们给出可构造具有良好纠错能力的CSS码的线性码对数量下界，证明通过随机化方法易于生成此类码对。随后我们证明CSS-T码呈现相反特性，并表明在非常自然的假设条件下，其码率与相对距离无法同时达到较大值。这部分回答了关于CSS-T码可行参数的开放性问题。最后通过埃尔米特曲线给出CSS-T码的简单构造方法。本文还从经典编码理论视角对CSS与CSS-T码进行了简明介绍。