Consider a (15,3) cyclic code. a) Show that g(D) = 1 +D3 + D + D + D12 is a generator polynomial of this code. [4 marks] b) Suppose a codeword has been transmitted across a channel and the received sequence is represented as the polynomial r(D) = 1 +D2 + DS + D + D +D14. Find the syndrome (in polynomial form). [5 marks] Consider a (15,3) cyclic code. a) Show that g(D) = 1 +D3 + D + D + D12 is a generator polynomial of this code. [4 marks] b) Suppose a codeword has been transmitted across a channel and the received sequence is represented as the polynomial r(D) = 1 +D2 + DS + D + D +D14. Find the syndrome (in polynomial form). [5 marks]