Given some choice of parameters $ [[n,k,d]] $ with $ n $ small, is there any computationally easy way to find all of (or at least many of) the stabilizer codes with those parameters?
For certain parameters this is easy, for example it is known that there is a unique stabilizer code corresponding to each of the parameters $ [[4,2,2]], [[5,1,3]], [[8,3,3]] $. And for many other choices of parameters $ [[n,k,d]] $ no codes exist at all, by the bounds given in https://arxiv.org/abs/quant-ph/9608006
But what about choices of parameters that are possible but not unique, such as $ [[5,1,2]] $?
But in general how do I write down stabilizer generators for small codes? I'm hoping there might be a nice way to get at least some of these using GUAVA? Along the lines of past answers from @unknown
Smallest distance 9 self-dual CSS code?
Example CSS codes and the properties "doubly even" and "self dual"
and even
Generators for $[[9,1,3]]$ linear quantum code
This question is partially inspired by another more recent question from @unknown about translating between stabilizer codes and graph codes
how to go from a stabilizer state to a graph
If graph states aren't the right approach then perhaps there is some way to write down these codes as (twisted) surface codes? https://quantumcomputing.stackexchange.com/a/37586/19675
