Stabilizer Codes with Exotic Local-dimensions

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.