The polynomial 1 + X⁷ has 1 + X + X³ and 1 + X² + X³ as primitive factors. In Example 10.3, we used 1 + X + X³ as the generator polynomial for a (7,4)1-lamming code. In this problem, we consider the adoption of 1 + X² + X³ as the generator polynomial. This should lead to a (7, 4) Hamming code that is different from the code analyzed in Example 10.3. Develop the encoder and syndrome calculator for the generator polynomial: g(X) = 1 + X² + X³ compare your results with those in Example 10.3.