1. Consider a binary Hamming (7,4,3) code with parity-check matrix 1 10 1 1 0 0 H=1101101 (a) What is the generator matrix G of the code? (b) Build an encoding look-up table with two columns where you list all the 16 com binations of 4 information bits x = B = (Bi B2 B3 B4) in the first column and the associated codewords c = xG = BG in the second column. (e) Build a hard-decision decoding lookup table with t wo colus: In the second column list all the 8 error vectors of Hamming weight up to 1 (no errors plus 7 single errors). In the first column list the associated syndrome vectors s = ?HT (d) Supposed that the received vector is F (o 101 0 1 0) i. Determine the syndrome vector 5 ii. Determine the most likely error vector e ii. Determine the most likely information bits B(B B, B B) 1. Consider a binary Hamming (7,4,3) code with parity-check matrix 1 10 1 1 0 0 H=1101101 (a) What is the generator matrix G of the code? (b) Build an encoding look-up table with two columns where you list all the 16 com binations of 4 information bits x = B = (Bi B2 B3 B4) in the first column and the associated codewords c = xG = BG in the second column. (e) Build a hard-decision decoding lookup table with t wo colus: In the second column list all the 8 error vectors of Hamming weight up to 1 (no errors plus 7 single errors). In the first column list the associated syndrome vectors s = ?HT (d) Supposed that the received vector is F (o 101 0 1 0) i. Determine the syndrome vector 5 ii. Determine the most likely error vector e ii. Determine the most likely information bits B(B B, B B)