Designs, Codes and Cryptography

, Volume 59, Issue 1, pp 119–130

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

Open AccessArticle

DOI: 10.1007/s10623-010-9469-6

Cite this article as:
Danielsen, L.E. & Parker, M.G. Des. Codes Cryptogr. (2011) 59: 119. doi:10.1007/s10623-010-9469-6


We show that (n, 2n) 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, 2n) 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 codesQuaternary codesClassificationGraphsCirculant codesFormally self-dual codes

Mathematics Subject Classification (2000)

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© The Author(s) 2010

Authors and Affiliations

  1. 1.Department of InformaticsUniversity of BergenBergenNorway