Sums of residues on algebraic surfaces and application to coding theory

DOI10.1016/j.jpaa.2009.03.009zbMath1174.14023arXiv0810.4112OpenAlexW2043131916MaRDI QIDQ734805

Alain Couvreur

Publication date: 13 October 2009

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

Full work available at URL: https://arxiv.org/abs/0810.4112

Mathematics Subject Classification ID

Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Arithmetic ground fields for surfaces or higher-dimensional varieties (14J20) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Related Items (4)

The dual minimum distance of arbitrary-dimensional algebraic-geometric codes ⋮ Differential codes on higher dimensional varieties via Grothendieck's residue symbol ⋮ Factoring bivariate polynomials using adjoints ⋮ Differential approach for the study of duals of algebraic-geometric codes on surfaces

Cites Work

• Algebraic function fields and codes
• Geometric construction of some families of two-class and three-class association schemes and codes from nondegenerate and degenerate Hermitian varieties
• Codes defined by forms of degree 2 on non-degenerate Hermitian varieties in \(\mathbb{P}^4(\mathbb{F}_q)\)
• The red book of varieties and schemes. Includes the Michigan lectures (1974) on ``Curves and their Jacobians.
• Error-correcting codes from higher-dimensional varieties
• Codes from flag varieties over a finite field
• Codes defined by forms of degree 2 on Hermitian surfaces and Sørensen's conjecture
• Error-correcting codes on low rank surfaces
• Codes Defined by Forms of Degree $2$ on Quadric Surfaces
• Algebraic geometry codes from higher dimensional varieties
• Modular curves, Shimura curves, and Goppa codes, better than Varshamov-Gilbert bound
• The weight hierarchy of higher dimensional Hermitian codes
• On the decoding of algebraic-geometric codes
• On the Structure and Ideal Theory of Complete Local Rings
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