Need a reference on period of LFSRs
Not all LFSRs have the property of maximum cycle length. In fact, those who do have this property are based on a primitive polynomial of order n. It is a basic property of the extension field $GF(2^n)$ which is "spanned" by this primitive polynomial. The LFSR merely iterates through all of the powers of the polynomial primitive root. 

Open a book on algebraic structures and cite the relevant part.