  Quantum error correction codes in continuous variables (also called CV codes,
or single-mode bosonic codes) have recently been identified to be a
technologically viable option for building fault-tolerant quantum computers.
The best-known examples are the GKP code and the cat-code, both of which were
shown to have some advantageous properties over any discrete-variable, or qubit
codes. It was recently shown that the cat-code, as well as other kinds of CV
codes, belong to a set of codes with common properties called
rotation-symmetric codes. We expand this result by giving a general description
of sets of codes with common properties, and rules by which they can be mapped
into one another, effectively creating a unified description of
continuous-variable codes. We prove that the properties of all of these sets of
codes can be obtained from the properties of the GKP code. We also show
explicitly how this construction works in the case of rotation-symmetric codes,
re-deriving known properties and finding new ones.
