I am looking for a small stabilizer code that protect one logical qubit from $X$ and $Z$ noise.
Maybe not necessarily all of the physical qubits.
Something that has a good tradeoff between number of detections and number of physical qubits.
I know about the Stean code, which use 7 qubits. I also know about the [[5,1,3]] code.
Is there a code with less physical qubit doing something similar?