Designs, Codes and Cryptography

, Volume 59, Issue 1–3, pp 119–130 | Cite as

Directed graph representation of half-rate additive codes over GF(4)

Open Access


We show that (n, 2 n ) additive codes over GF(4) can be represented as directed graphs. This generalizes earlier results on self-dual additive codes over GF(4), which correspond to undirected graphs. Graph representation reduces the complexity 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 of isodual and formally self-dual codes. We introduce new constructions of circulant and bordered circulant directed graph codes, and show that these codes will always be isodual. A computer search of all such codes of length up to 26 reveals that these constructions produce many codes of high minimum distance. In particular, we find new near-extremal formally self-dual codes of length 11 and 13, and isodual codes of length 24, 25, and 26 with better minimum distance than the best known self-dual codes.


Additive codes Quaternary codes Classification Graphs Circulant codes Formally self-dual codes 

Mathematics Subject Classification (2000)

94B05 05C30 



The authors would like to thank Jürgen Bierbrauer for helpful comments. This research was supported by the Research Council of Norway.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2010

Authors and Affiliations

  1. 1.Department of InformaticsUniversity of BergenBergenNorway

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