Use matrices to describe the full process of sending and receiving the message 01000101010 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. You should explicitly give all the matrices used in the process that is, write down all the matrices used to encode, check and decode the message.

To show how an error is corrected, show what happens when the message is received correctly except that there is an error in position (n + 6), where n = 3.