(1 point) Finally, in this problem, you get to put together everything you have learned! Consider the linear code C = {000000, 001011,010101,011110, 100110, 101101, 110011, 111000} . (a) What is the code length, message length, and Hamming distance of C? Code length: Message length: Hamming distance: (b) Find a generator matrix for C. Answer: G (c) Find a check matrix for C. Answer: H = (d) Using your generator matrix from part (b), encode the message 111 110 001. Encoded message: (e) Using your check matrix from part (c), make a syndrome table. (e) Using your check matrix from part (c), make a syndrome table. Error pattern: 000000 Error pattern: 100000 Error pattern: 010000 Error pattern: 001000 Error pattern: 000100 Error pattern: 000010 Error pattern: 000001 Syndrome: Syndrome: Syndrome: Syndrome: Syndrome: Syndrome: Syndrome () Decode the message 000011 101101 000100. For each code word, find the syndrome and the error pattern, then correct the error and decode. Code block: 000011 Syndrome: Error pattern: Corrected code block: Decoded message block: Code block: 101101 Syndrome: Error pattern: Corrected code block: Decoded message block: Code block: 000100 Syndrome: Error pattern: Corrected code block: Decoded message block: (1 point) Finally, in this problem, you get to put together everything you have learned! Consider the linear code C = {000000, 001011,010101,011110, 100110, 101101, 110011, 111000} . (a) What is the code length, message length, and Hamming distance of C? Code length: Message length: Hamming distance: (b) Find a generator matrix for C. Answer: G (c) Find a check matrix for C. Answer: H = (d) Using your generator matrix from part (b), encode the message 111 110 001. Encoded message: (e) Using your check matrix from part (c), make a syndrome table. (e) Using your check matrix from part (c), make a syndrome table. Error pattern: 000000 Error pattern: 100000 Error pattern: 010000 Error pattern: 001000 Error pattern: 000100 Error pattern: 000010 Error pattern: 000001 Syndrome: Syndrome: Syndrome: Syndrome: Syndrome: Syndrome: Syndrome () Decode the message 000011 101101 000100. For each code word, find the syndrome and the error pattern, then correct the error and decode. Code block: 000011 Syndrome: Error pattern: Corrected code block: Decoded message block: Code block: 101101 Syndrome: Error pattern: Corrected code block: Decoded message block: Code block: 000100 Syndrome: Error pattern: Corrected code block: Decoded message block