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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.
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