2. (40 points) 1) Confirm the possibility of a (5, 2) binary code that can correct all single-error received words Can this code correct all double errors? 2) For the (5, 2) binary systematic linear block code a) Choose a parity check matrix H b) Find the corresponding generator matrix G c Construct the code generated by this matrix d) How many single error patterns and double error patterns can this code correct? Verify that your code can correct all single error patterns by looking at the Hamming distance Construct a decoding table (syndromes) and corresponding correctable error patterns? e 2. (40 points) 1) Confirm the possibility of a (5, 2) binary code that can correct all single-error received words Can this code correct all double errors? 2) For the (5, 2) binary systematic linear block code a) Choose a parity check matrix H b) Find the corresponding generator matrix G c Construct the code generated by this matrix d) How many single error patterns and double error patterns can this code correct? Verify that your code can correct all single error patterns by looking at the Hamming distance Construct a decoding table (syndromes) and corresponding correctable error patterns? e