Consider the linear code C = {000000, 000111, 011001, 011110, 101011, 101100, 110010, 110101}. (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 011 111 001. 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 Error pattern: 000100 Error pattern: 000010 Error pattern: 000001 Syndrome: Syndrome: Syndrome: Syndrome: Syndrome: Syndrome: Syndrome: (1) Decode the message 111011 000111 010110. 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: 111011 Syndrome: Decoded message block: Code block: 000111 Syndrome: Decoded message block: Code block: 010110 Syndrome: Decoded message block: Error pattern: Corrected code block: Consider the linear code C = {000000, 000111, 011001, 011110, 101011, 101100, 110010, 110101}. (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 011 111 001. 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 Error pattern: 000100 Error pattern: 000010 Error pattern: 000001 Syndrome: Syndrome: Syndrome: Syndrome: Syndrome: Syndrome: Syndrome: (1) Decode the message 111011 000111 010110. 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: 111011 Syndrome: Decoded message block: Code block: 000111 Syndrome: Decoded message block: Code block: 010110 Syndrome: Decoded message block: Error pattern: Corrected code block