Question: Problem 5. (15 points) Suppose that C1 and C2 are binary linear cyclic codes of length 15, whose generator polynomials are 81 (x) = x8

Problem 5. (15 points) Suppose that C1 and C2 are binary linear cyclic codes of length 15, whose generator polynomials are 81 (x) = x8 + x + x + x4 + 1 and g2(x) = x8 +x7 +x5 + x4+x3 +x+ 1, respectively. Let C3 def CinC2 = { c : CEC] and c EC2} def COC2 = {atb : aEC1, beC2} a. Prove that C3 and C4 are linear cyclic codes. b. Find the generator polynomial of C3. c. Find the generator polynomial of C4

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