Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A characterization of $\mathbb{Z}_2\mathbb{Z}_2[u]$-linear codes   We prove that the class of $\Z_2\Z_2[u]$-linear codes is exactly the class of
$\Z_2$-linear codes with automorphism group of even order. Using this
characterization, we give examples of known codes, e.g. perfect codes, which
has a nontrivial $\Z_2\Z_2[u]$ structure. We also exhibit an example of a
$\Z_2$-linear code which is not $\Z_2\Z_2[u]$-linear. Also, we state that
duality of $\Z_2\Z_2[u]$-linear codes is the same that duality of $\Z_2$-linear
codes.
  Finally, we prove that the class of $\Z_2\Z_4$-linear codes which are also
$\Z_2$-linear is strictly contained in the class of $\Z_2\Z_2[u]$-linear codes.

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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg