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?
2026-04-01 08:00:45.1775030445
u | u + v Coding
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A generator matrix of the $(C_1 \mid C_1 + C_2)$ code is given by $$ \begin{pmatrix} G_1 & G_1 \\ 0 & G_2 \end{pmatrix}. $$