I saw in the literature claims that no single-shot 3D stabilizer code is known and that only 3D subsystem codes are known to have this feature.
However, isn't the topological cluster state (also known as Raussendorf's cube or RHG cube) a single-shot stabilizer code since any qubit is measured only once?
I believe this is just a matter of definition, in some sense the topological state is a single-shot code.
One difference between the topological cluster state and single-shot 3D codes is that the size of the topological cluster state grows with respect to how long you want to protect encoded information, while for a single-shot code like the 3D subsystem toric code the number of qubits is independent of how long you want to protect encoded information.
