Can the marked qubit be associated only with half of the register? I mean if I can ask the oracle if the $2$ low qubits from a $4$ qubit register have a certain value.
I ask this to know if I can bit-append for example names and telephones into one register, so I can entangle the marked qubit with CNOT gates only with one half of register qubits which are the telephones, so when I seek a telephone the oracle amplifies the state associated with the qubit marked.
There will be $N\times N$ states in the register initialized all to $0$ except the $N$ that are name-telephone equally with HADAMARD to get $1$ on the states' sumatory module.