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We show that (n,2^n) additive codes over GF(4) can be represented as directedgraphs. This generalizes earlier results on self-dual additive codes overGF(4), which correspond to undirected graphs. Graph representation reduces thecomplexity of code classification, and enables us to classify additive (n,2^n)codes over GF(4) of length up to 7. From this we also derive classifications ofisodual and formally self-dual codes. We introduce new constructions ofcirculant and bordered circulant directed graph codes, and show that thesecodes will always be isodual. A computer search of all such codes of length upto 26 reveals that these constructions produce many codes of high minimumdistance. In particular, we find new near-extremal formally self-dual codes oflength 11 and 13, and isodual codes of length 24, 25, and 26 with betterminimum distance than the best known self-dual codes.

Directed Graph Representation of Half-Rate Additive Codes over GF(4)