Problem 5. (15 points) Suppose that (Cl and (C; are binary linear cyclic codes of length 15, whose generator polynomials are g1(x) = x3 + x7 + x6 + x4 + 1 and 32(1):): 3:3 + x7 + x5 + x4 + x3 + x + 1, respectively. Let Q d=ef C1 0C2 = {g:gEC1andEC2} C4 d=ef C1$C2 = {a+b : 96631499} 3. Prove that C3 and (C4 are linear cyclic codes. b. Find the generator polynomial of (C3. c. Find the generator polynomial of (C4