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Directed Graph Representation of Half-Rate Additive Codes over GF(4)
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@MISC{Danielsen_directedgraph,
author = {Lars Eirik Danielsen and Matthew G. Parker},
title = {Directed Graph Representation of Half-Rate Additive Codes over GF(4)},
year = {}
}
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Abstract
Abstract. We show that (n, 2 n, d) 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 greatly reduces the complexity of code classification, and enables us to classify additive (n, 2 n, d) 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. 1
Keyphrases
directed graph representation half-rate additive code self-dual code undirected graph many code computer search known self-dual code isodual code graph code directed graph additive code self-dual additive code code classification minimum distance high minimum distance new construction graph representation
