Classification of linear codes exploiting an invariant

We consider the problem of computing the equivalence classes of a set of linear codes. This problem arises when new codes are obtained extending codes of lower dimension. We proposed a technique that, exploiting a simply computed invariant, allows us to reduce the computational complexity of the classification process. These classifications enabled us to solve the packing problem for NMDS codes for q=7,8,9. The same technique can be applied to the problem of the classification of other structures.