2) Consider a (7, 4) Hamming code with the following generating matrix: 1 1 0 1 0 0 0 0 0 1 1 0 1 0 0 G= 1 1 1 0 0 1 1 0 1 0 1 0 0 0 1 a. Find the generator polynomial the code. (2 Marks). b. Find the generator matrix of dual code of this code (2 Marks). c. Is the dual code a perfect code? Why? (2 Marks). d. Find the generator polynomial of the dual code. (2 Mark)