Traditional stabilizer codes operate over prime power local-dimensions. In this work we extend the stabilizer formalism using the local-dimension-invariant setting to import stabilizer codes from these standard local-dimensions to other cases. In particular, we show that any traditional stabilizer code can be used for analog continuous-variable codes, and consider restrictions in phase space and discretized phase space. This puts this framework on equivalent footing as traditional stabilizer codes. Following this, using extensions of the prior ideas, we show that a stabilizer code originally designed with a finite field local-dimension can be transformed into a code with the same $n$, $k$, and $d$ parameters for any integral domain ring. This is of theoretical interest and can be of use for systems whose local-dimension is better described by mathematical rings, for which this permits the use of traditional stabilizer codes for protecting their information as well.

翻译：传统稳定子码作用于素数幂局域维数。本文利用局域维数不变框架扩展了稳定子形式体系，将标准局域维数下的稳定子码推广至其他情形。特别地，我们证明任何传统稳定子码均可用于模拟连续变量码，并考虑相空间及离散化相空间中的约束条件，从而使该框架与传统稳定子码处于同等地位。基于上述思想的扩展，我们进一步证明，原本基于有限域局域维数设计的稳定子码，可转化为任意整环上具有相同参数 $n$、$k$、$d$ 的码。该结果兼具理论价值，且适用于局域维数更适合用数学环描述的系统——在此类系统中，该理论允许使用传统稳定子码保护其信息。