# Is a cross-correlation property of Gold code independent to modulation?

Gold code is known to have a good cross-corrleation property, i.e., a high cross-correlation value shows iff two sequences are the same.

I wonder whether it is independent to modulation, e.g., BPSK, QPSK, M-PSK, M-QAM, when Gold code is applied to wireless communication.

My naive guess that, since mapping from a binary Gold code to a modulated signal is 1-to-1, so the answer is yes, independent to modulation.

P.S. I'm a bit confused whether this question is proper to EE.stackexchange or math.stackexchange.