I'm searching for a circuit to generate, starting from the $|00\, ...\,0\rangle$ state, an arbitrary superposition of all states with either even or odd parity. The gate choice is irrelevant for now, but sticking with single qubit gates and controlled rotations would be preferrable.
For example, for 3 qubits, I want to be able to generate the states $$ |\mathrm{odd}\rangle = a|001\rangle + b|010\rangle + c |100\rangle + d|111\rangle $$ and $$ |\mathrm{even}\rangle = a|000\rangle + b|011\rangle + c |101\rangle + d|110\rangle $$ where $a,b,c,d$ are freely chosen complex values satisfying the condition of normalization.