Parity check and Hamming codes

8. The parity check bits of (8,4) block code are generated by c5=d1d2d4c6=d1d2d3c7=d1d3d4c8=d2d3d4 where d1,d2,d3 and d4 are the message bits. a) Find the generator matrix and the parity check matrix for this code. b) Correct the following received code vector 10101001 c) Draw the encoder circuit and syndrome circuit 9. The generator polynomial of a (15,11) hamming code is given by G(P)=P4+P+ 1. i) Find the codeword for the message ' 10010100101 using systematic form. ii) Illustrate the encoding procedure with the message vector given in part (i) with a neat sketch