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Sums of residues on algebraic surfaces and application to coding theory

Abstract : In this paper, we study residues of differential 2-forms on a smooth algebraic surface over an arbitrary field and give several statements about sums of residues. Afterwards, using these results we give a new construction of algebraic-geometric codes which can be regarded as an extension to surfaces of the well-known construction of differential codes on curves. We also study some properties of these codes and extend to them some known properties for codes on curves.
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https://hal.inria.fr/inria-00540021
Contributor : Alain Couvreur Connect in order to contact the contributor
Submitted on : Wednesday, December 1, 2010 - 2:20:44 PM
Last modification on : Wednesday, June 1, 2022 - 5:01:04 AM
Long-term archiving on: : Wednesday, March 2, 2011 - 2:29:36 AM

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Alain Couvreur. Sums of residues on algebraic surfaces and application to coding theory. Journal of Pure and Applied Algebra, Elsevier, 2009, 213 (12), pp.2201-2223. ⟨10.1016/j.jpaa.2009.03.009⟩. ⟨inria-00540021⟩

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