Differential approach for the study of duals of algebraic-geometric codes on surfaces

DOI10.5802/jtnb.752zbMath1278.14036arXiv0905.2341OpenAlexW2964335538WikidataQ115158940 ScholiaQ115158940MaRDI QIDQ449692

Alain Couvreur

Publication date: 31 August 2012

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0905.2341

zbMATH Keywords

algebraic surfacesalgebraic geometry codesdifferentials

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Related Items

A short proof that all linear codes are weakly algebraic-geometric using Bertini theorems of B. Poonen, On the geometry of Hermitian one-point codes, Differential codes on higher dimensional varieties via Grothendieck's residue symbol

Uses Software

• MinT
• Code Tables

Cites Work

• On the characteristic polynomials of the Frobenius endomorphism for projective curves over finite fields
• Sums of residues on algebraic surfaces and application to coding theory
• Linear codes and modular curves
• Codes defined by forms of degree 2 on Hermitian surfaces and Sørensen's conjecture
• Error-correcting codes on low rank surfaces
• Bertini theorems over finite fields
• Algebraic Function Fields and Codes
• Codes Defined by Forms of Degree $2$ on Quadric Surfaces
• Geometric reed-solomon codes of length 64 and over 65 over F/sub 8/
• MinT: A Database for Optimal Net Parameters
• On generalized ReedMuller codes and their relatives
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