Let C be a linear code, with generator matrix G in standard form.
Construct G* from G by adding an extra column so that every row of G* has an even number of 1's.
Let C* be the linear code with generator matrix G*.

Let H be the parity check matrix for C. Show that the matrix H* obtained from H by adding a column of 0's and then a row of 1's is a parity check matrix for C*