Consider the linear code C = {000000,001110, 010011, 011101, 100101, 101011, 110110, 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 101 011010. Encoded message: (e) Using your check matrix from part (c), make a syndrome table. Error pattern: 000000 Error pattern: 100000 Error pattern: 010000 Error pattern: 001000 Syndrome: Syndrome: Syndrome: Syndrome: Syndrome: Syndrome: Error pattern: 000100 Error pattern: 000010 Error pattern: 000001 Syndrome: (1) Decode the message 011011 100001 111000. For each code word, find the syndrome and the error pattern, then correct the error and decode. Error pattern: Corrected code block: Error pattern: Corrected code block: Code block: 011011 Syndrome: Decoded message block: Code block: 100001 Syndrome: Decoded message block: Code block: 111000 Syndrome: Decoded message block: Error pattern: Corrected code block