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 an equivalent footing as traditional stabilizer codes. Following this, using extensions of 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. This is of theoretical interest and can be of use for systems whose local-dimension is better described by mathematical rings, which permits the use of traditional stabilizer codes for protecting their information as well.

翻译：传统稳定子码在素数幂局部维数上运行。本文利用局部维数不变性框架扩展稳定子形式体系，将稳定子码从这些标准局部维数导入到其他情形。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相空间中的约束条件，从而使该框架与传统稳定子码具有等价地位。在此基础上，通过扩展既有思想，我们证明最初基于有限域局部维数设计的稳定子码可转化为具有相同$n$、$k$、$d$参数且适用于任意整环的码。这一结论具有理论意义，且可用于局部维数更适合用数学环描述的系统，从而允许利用传统稳定子码保护此类系统中的信息。