4. Let C' be the code with generator matrix 1 1 1 1 0 0 0 11 00 1 0 0 10 1 0 0 1 0 0110 0 0 1 and parity check matrix 1 0 0 1 1 1 0 H=10 1 0 1 1 0 1 Notice that C is a binary Hamming code with r-3. Therefore the minimum distance of C is d=3. (a) Explain why 0000000, 1000000, 0100000, 0010000, 0001000, 0000100, 0000010, 0000001 can be a taken as a set of coset leaders for C (b) Calculate the syndrome of each coset leader, and assemble the coset leaders and their syndromes into a syndrome lookup table1 (Do not calculate a full standard array for this code.) (c) Use syndrome decoding to correct the errors in the received words 1100010 and 0001010 4. Let C' be the code with generator matrix 1 1 1 1 0 0 0 11 00 1 0 0 10 1 0 0 1 0 0110 0 0 1 and parity check matrix 1 0 0 1 1 1 0 H=10 1 0 1 1 0 1 Notice that C is a binary Hamming code with r-3. Therefore the minimum distance of C is d=3. (a) Explain why 0000000, 1000000, 0100000, 0010000, 0001000, 0000100, 0000010, 0000001 can be a taken as a set of coset leaders for C (b) Calculate the syndrome of each coset leader, and assemble the coset leaders and their syndromes into a syndrome lookup table1 (Do not calculate a full standard array for this code.) (c) Use syndrome decoding to correct the errors in the received words 1100010 and 0001010