1. In this problem, you are going to design your own (6,3) single error-correcting code (SEC) and do a lot of manipulations with such. (a) Design a (6,3) single error-correcting linear block code (SEC) by giving G, H, and the set of codewords C for such. (There are many potential solutions. Do not use the one from class or one that matches your friends' solutions!) (b) Find the minimum distance dmin of your code. (c) Using your number for dmin from (b), identify dmin columns of H that sum to zero. d) Find the (full) standard array and identify the coset leaders. (Yes. I know this is going to take a little bit of time.) (e) Suppose the information bits are (011) and the error pattern is (010000). Do the following: Find the transmitted codeword Find the received vector. Find the syndrome. List all of the possible error patterns that could have occurred given your syndrome, and, for each, identify the codeword you would output if that were the error pattern. (This should be a table with 8 rows; in each row, you should have an error pattern and the corresponding codeword you would output.) Give the output codeword if you choose the error pattern corresponding to the coset leader. Was the correct codeword identified? 1. In this problem, you are going to design your own (6,3) single error-correcting code (SEC) and do a lot of manipulations with such. (a) Design a (6,3) single error-correcting linear block code (SEC) by giving G, H, and the set of codewords C for such. (There are many potential solutions. Do not use the one from class or one that matches your friends' solutions!) (b) Find the minimum distance dmin of your code. (c) Using your number for dmin from (b), identify dmin columns of H that sum to zero. d) Find the (full) standard array and identify the coset leaders. (Yes. I know this is going to take a little bit of time.) (e) Suppose the information bits are (011) and the error pattern is (010000). Do the following: Find the transmitted codeword Find the received vector. Find the syndrome. List all of the possible error patterns that could have occurred given your syndrome, and, for each, identify the codeword you would output if that were the error pattern. (This should be a table with 8 rows; in each row, you should have an error pattern and the corresponding codeword you would output.) Give the output codeword if you choose the error pattern corresponding to the coset leader. Was the correct codeword identified