Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Directed Graph Representation of Half-Rate Additive Codes over GF(4)   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.

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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int