Sums of residues on algebraic surfaces and application to coding theory

Details Sums of residues on algebraic surfaces and application to coding theory Sums of residues on algebraic surfaces and application to coding theory

2008-10-22

arxiv.org/abs/0810.4112v1

Journal of Pure and Applied Algebra, vol 213 number 12, pages 2201-2223, 2009

Mathematics

Algebraic Geometry

31 pages

Scientific paper

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.

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