Use matrices to describe the full process of sending and receiving this message using a Hamming (15, 11) code, including how the message is encoded, how the parity is checked, how an error is corrected and how the original message is recovered, giving in full all the necessary matrices. Demonstrate the error-correction operation by changing the fifth bit of your encoded message and showing how the correct message can be recovered. Show what happens if the first and second bits of your encoded message are both changed, and comment on your answer.

Fig: 1