In the Hamming (7, 4) code an additional parity is bit added (as bit 8). This equals the sum of all the other codeword bits (data and parity). From the Venn diagram, and for the matrix H we see that it should now be 8 4 and to make the checksum work for every circle the matrix should have an additional row added, the entries of which should be the sum of all previous rows in that column - and this turms out to be always a 1. A last column is added and this is all zeros except the last entry is 1.

1. Find the corresponding code generator matrix G.

2. Show that this code has minimum distance 4.

3. Show that this code can detect two errors and distinguish this from the single error case.