I need a reference for the fact that each LFSR with XOR operation has a period of $2^m-1$ excluding zero state and every LFSR with XNOR operations has the same period excluding all ones state.
I want to cite it when I'm writing about the usage of LFSR in a paper, I've found some references but they avoid a proof and all of them include only the case of XOR operations.
Since LFSRs are mostly used in signal processing I ask it here.
Edit: I know that the feedback polynomial should be primitive.