engineering recuitment GATE ECE 2023-24 Test Series Communication Systems Fundamentals of Error Correction Hamming Codes
A digital transmission system uses a (7, 4) systematic linear Hamming code for transmitting data over a noisy channel. If three of the message-codeword pairs in this code (mi ; ci), where ci is the codeword corresponding to the ith message mi, are known to be (1 1 0 0 ; 0 1 0 1 1 0 0), (1 1 1 0 ; 0 0 1 1 1 1 0) and (0 1 1 0 ; 1 0 0 0 1 1 0), then which of the following is a valid codeword in this code?
1
1 0 1 1 0 1 0
2
0 1 1 0 1 0 0
3
0 0 0 1 0 1 1
4
1 1 0 1 0 0 1