The question is:

A group code has a generator matrix:

1 0 0 1 0 0 1
0 1 0 0 1 1 0
0 0 1 0 1 0 1

List the codewords and state how many errors are detected and how many are corrected by this code, giving reasons for your answers.

Write down the parity check matrix and a table of syndromes for this code for all possible single digit errors in transmission


How do I do this? I can see that the first three rows and columns is a 3 x 3 identity matrix but I can't remember what this has to do with anything. Please can you help me on this question.

Thank you