Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Every Binary Self-Dual Code Arises From Hilbert Symbols   In this paper we construct binary self-dual codes using the \'etale
cohomology of $\mathbb{Z}/2$ on the spectra of rings of $S$-integers of global
fields. We will show that up to equivalence, all self-dual codes of length at
least 4 arise from Hilbert pairings on rings of $S$-integers of $\Q$. This is
an arithmetic counterpart of a result of Kreck and Puppe, who used cobordism
theory to show that all self-dual codes arise from Poincar\'e duality on real
three manifolds.

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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: q-fin
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: eess