Ignore all the numbers theyre wrong answers
Problem LIST Next Problem (1 point) Finally, in this problem, you get to put together everything you have learned! Consider the linear code C - {000000,001111, 010101, 011010, 100011, 101100, 110110, 111001). (a) What is the code length, message length, and Hamming distance of C? Code length: 6 Message length: 8 Hamming distance: 4 (b) Find a generator matrix for C 0 1 0 1 Answer: G 0 1 0 0 O (c) Find a check matrix for C. 0 1 0 0 Answer: H 1 1 0 0 1 0 1 0 0 1 (d) Using your generator matrix from part (b), encode the message 011 010 101 Encoded message: 010000 000010 001000 (e) Using your check matrix from part (c), make a syndrome table Syndrome 000 Syndrome 111 Syndrome 011 Error pattern: 000000 Error pattern: 100000 Error pattern: 010000 Error pattern: 001000 Error pattern: 000100 Error pattern: 000010 Error pattern: 000001 Syndrome 101 Syndrome 100 Syndrome 010 Syndrome 001 (1) Decode the message 110011 110110 000100. For each code word, find the syndrome and the error pattern, then correct the error and decode Code block: 110011 Syndrome: 011 Error pattern: 010000 Corrected code block 100011 Decoded message block Code block 110110 Syndrome: 010 Error pattern 000010 Corrected code block 110100 Decoded message block Code block: 000100 Syndrome 100 Error pattern 000100 Corrected code block 000000 Decoded message block Problem LIST Next Problem (1 point) Finally, in this problem, you get to put together everything you have learned! Consider the linear code C - {000000,001111, 010101, 011010, 100011, 101100, 110110, 111001). (a) What is the code length, message length, and Hamming distance of C? Code length: 6 Message length: 8 Hamming distance: 4 (b) Find a generator matrix for C 0 1 0 1 Answer: G 0 1 0 0 O (c) Find a check matrix for C. 0 1 0 0 Answer: H 1 1 0 0 1 0 1 0 0 1 (d) Using your generator matrix from part (b), encode the message 011 010 101 Encoded message: 010000 000010 001000 (e) Using your check matrix from part (c), make a syndrome table Syndrome 000 Syndrome 111 Syndrome 011 Error pattern: 000000 Error pattern: 100000 Error pattern: 010000 Error pattern: 001000 Error pattern: 000100 Error pattern: 000010 Error pattern: 000001 Syndrome 101 Syndrome 100 Syndrome 010 Syndrome 001 (1) Decode the message 110011 110110 000100. For each code word, find the syndrome and the error pattern, then correct the error and decode Code block: 110011 Syndrome: 011 Error pattern: 010000 Corrected code block 100011 Decoded message block Code block 110110 Syndrome: 010 Error pattern 000010 Corrected code block 110100 Decoded message block Code block: 000100 Syndrome 100 Error pattern 000100 Corrected code block 000000 Decoded message block
