Back in my days as a CPU logic designer, I actually worked on a scientific mainframe where the MIB came by and said "We'll buy some if you add a vector pop count."
Anyway.... if you have cipher text that has been scrambled by a linear-feedback shift register, you can take two copies of the cipher text, shift one copy by N bits, XOR them together, and do a pop count on the result. Repeat for bunch of different N's. For some N that corresponds to the length of the LFSR the auto-correlation will be much better. So now you have at least that to go on... of course you don't know the feedback equation and you don't know the initialization constant, but you have the start of a handle.
Anyway.... if you have cipher text that has been scrambled by a linear-feedback shift register, you can take two copies of the cipher text, shift one copy by N bits, XOR them together, and do a pop count on the result. Repeat for bunch of different N's. For some N that corresponds to the length of the LFSR the auto-correlation will be much better. So now you have at least that to go on... of course you don't know the feedback equation and you don't know the initialization constant, but you have the start of a handle.