Geodesic
Every binary self-dual code arises from Hilbert symbols
Homology, homotopy, and applications, Tome 14 (2012) no. 2, pp. 189-196.

Voir la notice de l'article provenant de la source International Press of Boston

In this paper we construct binary self-dual codes using the étale cohomology of $\mu_2$ 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 $\mathbb{Q}$. 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 Poincaré; duality on real three manifolds.
DOI : 10.4310/HHA.2012.v14.n2.a11
Classification : 11T71, 14F20, 14G50, 94B05
Keywords: binary self-dual code, $S$-integer, étale cohomology 
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     title = {Every binary self-dual code arises from {Hilbert} symbols},
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     pages = {189--196},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2012.v14.n2.a11/}
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Ted Chinburg; Ying Zhang. Every binary self-dual code arises from Hilbert symbols. Homology, homotopy, and applications, Tome 14 (2012) no. 2, pp. 189-196. doi : 10.4310/HHA.2012.v14.n2.a11. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2012.v14.n2.a11/

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