Suppose you are given a linear code with generator matrix $G$ and parity check matrix $H$. The following is a list of ways you might modify your code. For each, determine the possible effect on the minimum distance.
Remove a row from $G$.
Remove a row from $H$.
Remove a column from $G$.
Perform elementary row operations on $H$.
My understanding is that:
- Removing a row from $G$ --> reducing the dimension $k$ --> possibly increase/decrease the min distance, but not sure if increasing or decreasing.
- Same as 1
- Removing a column from $G$ --> decreasing the length $n$ of the codewords --> decreasing the weight of codewords --> decreasing min distance $d$.
- Performing elementary row operations on $H$ --> we get the equivalent $H'$ --> nothing changes --> not affecting the min distance.
Can anyone please point out if I am wrong or add more comments? Thanks.