Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Self-dual 2-quasi-cyclic Codes and Dihedral Codes   We characterize the structure of 2-quasi-cyclic codes over a finite field F
by the so-called Goursat Lemma. With the characterization, we exhibit a
necessary and sufficient condition for a 2-quasi-cyclic code being a dihedral
code. And we obtain a necessary and sufficient condition for a self-dual
2-quasi-cyclic code being a dihedral code (if charF = 2), or a consta-dihedral
code (if charF odd). As a consequence, any self-dual 2-quasi-cyclic code
generated by one element must be (consta-)dihedral. In particular, any
self-dual double circulant code must be (consta-)dihedral. Also, we show a
necessary and sufficient condition that the three classes (the self-dual double
circulant codes, the self-dual 2-quasi-cyclic codes, and the self-dual
(consta-)dihedral codes) are coincide each other.

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The categories of this paper are: supr-con
3
The categories of this paper are: physics
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The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga