In this work, we study quantum error-correcting codes obtained by using Steane-enlargement. We apply this technique to certain codes defined from Cartesian products previously considered by Galindo et al. (IEEE Trans Inf Theory 64(4):2444–2459, 2018. https://doi.org/10.1109/TIT.2017.2755682). We give bounds on the dimension increase obtained via enlargement, and additionally give an algorithm to compute the true increase. A number of examples of codes are provided, and their parameters are compared to relevant codes in the literature, which shows that the parameters of the enlarged codes are advantageous. Furthermore, comparison with the Gilbert–Varshamov bound for stabilizer quantum codes shows that several of the enlarged codes match or exceed the parameters promised by the bound.

中文翻译：

---

关于笛卡尔积点集的量子码的Stean展开

在这项工作中，我们研究通过使用Steane放大获得的量子纠错码。我们将此技术应用于由Galindo等人先前考虑的笛卡尔乘积定义的某些代码。（IEEE Trans Inf Theory 64（4）：2444-2459，2018.https：//doi.org/10.1109/TIT.2017.2755682）。我们给出了通过放大获得的尺寸增加的界限，并另外给出了计算真实增加的算法。提供了许多代码示例，并将它们的参数与文献中的相关代码进行了比较，这表明放大代码的参数是有利的。此外，与稳定子量子码的吉尔伯特-瓦尔沙莫夫界线的比较表明，一些扩展的码匹配或超过了界线所承诺的参数。