On the classification of self-dual additive codes over GF(9)

Additive codes over GF(9) that are self-dual with respect to the Hermitian trace inner product have previously been classified up to length 8. In this paper, all codes of length 9 and 10 are classified, using a new algorithm that combines two graph representations of codes. First, the search space is reduced by the fact that every self-dual additive code can be mapped to a weighted graph. Then a different graph is described that transforms the problem of code equivalence into a problem of graph isomorphism.