C is a binary linear code
C = {00000000, 01101111, 11011000, 11111101, 10010010, 00100101, 01001010, 10110111}
I am trying to find two distinct generator matrices for C. I understand that generator matrices will involve 3 different codewords from C (due to dimension =3) and they need to form a basis, therefore they are linearly independent of each other. However i still can not manage to find two distinct generator matrices.
Any help would be much appreciated