Assume that we have a linear (7, 4) code, where the codewords corresponding to messages u = [1000], [0100], [0010], and [0001] are given as Message

Assume that we have a linear (7, 4) code, where the codewords corresponding to messagesu = [1000], [0100], [0010], and [0001] are given asMessage Codeword1 0 0 0 → 1 1 0 1 0 0 00 1 0 0 → 0 1 1 0 1 0 00 0 1 0 → 0 0 1 1 0 1 00 0 0 1 → 0 0 0 1 1 0 1(a) Determine all codewords in this code.(b) Determine the minimum distance, dmin, and how many errors, t , the code can correct.(c) The code above is not in systematic form. Calculate the generator matrix G for the correspondingsystematic code.(d) Determine the parity check matrix H, such that HG^T = 0.