u | u + v Coding G1 is generator of C1 and G2 is generator of C2. If C is c1 || c1 + c2 then how do you find the generator and parity-check of C?
I have tried two examples and I see a pattern in the G and H of C. I think I am able to generalize it as well. I have also tried with row and column variables but cannot get this to generalize. Any ideas/pointers/thoughts/references?

A generator matrix of the $(C_1 \mid C_1 + C_2)$ code is given by
$$
\begin{pmatrix}
G_1 & G_1 \\
0 & G_2
\end{pmatrix}.
$$
