8 bit linear feedback shift register Non-zero coefficients

Question

An 8-bit linear feedback shift register with connection polynomial C(X) = 1+aX +bX^2 +cX^3 +dX^4 +eX^5 + fX^6 +gX^7 +hX^8 is used to generate a pseudo-random binary sequence. This pseudo-random sequence is used as the enciphering key of a stream cipher. It is known that when the cipher is applied to the plaintext string [0,0,0,1,0,0,0,0,1,1,0,0,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,1,0,1] the corresponding ciphertext string is [0,1,0,0,0,1,1,0,0,0,0,0,0,0,1,0,1,1,1,0,0,1,1,1,0,1,0,0,1,1]. Determine the coefficients of the connection polynomial

Answer 1

Determine the key bits first.

Then write down the equations on $a, \ldots h$. Solve.