What is a linear code? What is a parity check matrix for a linear code? What is the minimum distance $d(C)$ for a linear code $C ?$

If $C_{1}$ and $C_{2}$ are linear codes having a certain relation (which you should specify), define the bar product $C_{1} \mid C_{2}$. Show that

$$d\left(C_{1} \mid C_{2}\right)=\min \left\{2 d\left(C_{1}\right), d\left(C_{2}\right)\right\}$$

If $C_{1}$ has parity check matrix $P_{1}$ and $C_{2}$ has parity check matrix $P_{2}$, find a parity check matrix for $C_{1} \mid C_{2}$.