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Sums of residues on algebraic surfaces and application to coding theory (0810.4112v1)
Published 22 Oct 2008 in math.AG, cs.IT, and math.IT
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 construct algebraic-geometric codes which are an extension to surfaces of the well-known differential codes on curves. We also study some properties of these codes and extend to them some known properties for codes on curves.