Coding Theory in Mathematics Problem, please solve problem 4 and then problem 5, these two questions are connected. Thank you!

PROBLEM 4. Let C C 25 have the generator matrix 0 010 G = 0 1 0 1 1 0 1 0 (a) Construct the standard array for C. (b) If the word 10100 is received, explain its decoding using the standard array. PROBLEM 5. Let C be the code from the previous problem. (a) Find the parity check matrix H. (b) Construct the syndrome lookup table with two columns: the syndrome and coset leader for each coset. (c) Explain syndrome decoding of the word 10100