I have a problem in which I can estimate the minimum distance needed for my linear code to be quite large, around 400-500. I also have a target k value of $k=32$. The value for n is flexible by design but should be around 1000. Based on papers I've read it seems this distance should be theoretically reachable.
Basically from these parameters I want to produce a generator matrix G.
I've been reading about building new codes from existing codes and it seems there are two options for what I want to do:
- puncture existing code
Start with something like Hadamard code and delete columns from its generator matrix until I reach my minimum weight and an acceptable $n$. This is a (n=$2^k$, k) code though so for $k=32$ it seems to have high computational complexity.
- extend existing code
Start with a smaller, known code, such as a BCH code and add columns to its generator matrix until I hit my target distance. At a glance this method seems more efficient.
I'm leading towards the latter approach, but the question is how to do it? My hope is to produce a Matlab code which can produce G for me.