A parity check matrix H contains r rows and n columns. The columns of H have odd weight vectors of weight 1, 3, 5, etc. Note that n and r correspond to the length of the code and the number of check bits. For a given n the smallest r is chosen such that the total number of such column vectors is equal to n.

(a) For n = 16 find the value of r and show the H matrix.

(b) Show that this code is capable of correcting single errors and detecting double errors.

(c) Find the corresponding G matrix.