I'm studying Neuroscience and don't have any background of coding theory. During my experiment, I got exciting result and I want to know if there is any theory for the maximum number of binary codewords length n, specific distance d (not minimum) and certain number of 1 (if the codeword is consist of 1 or 0). Hamming bound or Plotkin bound might be helpful but they don't restrict the number of 1 in codewords.
For example, If there is 100 neurons and 30 neurons are activated. The other day, 30 neurons out of 100 are activated but not the same neuron with the day before. If I represent the situation with binary and found that their distance is 40 (or their would be range from 35 to 45). I want to know the number of permutation set which satisfy the observation result.
Maybe it could be think as a problem that estimating a area from a point on a sphere with specific radius.
It would be grateful to give me reference or related documents. Thanks.