Time-reversal-invariant logical qubits on an odd number of spins have automatically scalar even-weight Pauli errors, so single-qubit error detection implies correction and every such code has odd distance.
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Time-Reversal Selection Rules for Quantum Error Correction
Time-reversal-invariant logical qubits on an odd number of spins have automatically scalar even-weight Pauli errors, so single-qubit error detection implies correction and every such code has odd distance.