I am being given chip sequences for four stations A, B, C and D as follows, all of which are orthogonal with each other, i.e. AB=0 AC=0 AD=0 BC=0 BD=0 CD=0. I am trying to find two more sequences, E and F that also provide orthogonality with the previous stations. It is easy enough to find a vector orthogonal to each of these individually, but as a whole, it is a puzzle i just can not solve.
A(-1,-1,-1,+1,+1,-1,+1,+1),
B(-1,-1,+1,-1,+1,+1,+1,-1),
C(-1,+1,-1,+1,+1,+1,-1,-1),
D(-1,+1,-1,-1,-1,-1,+1,-1)
EDIT: I know that these type of vectors are called Walsh codes and there is a method of generating them, and a corresponding 'Walsh matrix' however, generating compatible codes from existing codes is something beyond me.