Differential codes on higher dimensional varieties via Grothendieck's residue symbol

DOI10.1016/j.jpaa.2023.107535arXiv2009.09311OpenAlexW3087198710MaRDI QIDQ6185305

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Publication date: 8 January 2024

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.09311

zbMATH Keywords

algebraic geometric codesGrothendieck residue symboldifferential codes

Mathematics Subject Classification ID

Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Cites Work

• The dual minimum distance of arbitrary-dimensional algebraic-geometric codes
• Differential approach for the study of duals of algebraic-geometric codes on surfaces
• Sums of residues on algebraic surfaces and application to coding theory
• Hyperplane sections of determinantal varieties over finite fields and linear codes
• Toric complete intersection codes
• Residues and duality. Lecture notes of a seminar on the work of A. Grothendieck, given at Havard 1963/64. Appendix: Cohomology with supports and the construction of the \(f^!\) functor by P. Deligne
• Bertini theorems over finite fields
• Algebraic Function Fields and Codes
• Algebraic geometry codes from higher dimensional varieties
• An Algebraic Approach to Grothendieck's Residue Symbol
• On the decoding of algebraic-geometric codes
• Codes from Jacobian surfaces
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