Codes from Jacobian surfaces

DOI10.1090/conm/686/13780zbMath1369.94612arXiv1503.07903OpenAlexW1843712687MaRDI QIDQ5346822

Safia Haloui

Publication date: 29 May 2017

Published in: Arithmetic, Geometry, Cryptography and Coding Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.07903

zbMATH Keywords

abelian varietiesalgebraic-geometry codesnumber of rational pointsminimum Hamming distanceJacobian surfaces

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Families, moduli of curves (algebraic) (14H10) Varieties over finite and local fields (11G25) Subvarieties of abelian varieties (14K12) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Related Items (2)

Differential codes on higher dimensional varieties via Grothendieck's residue symbol ⋮ Algebraic geometry codes over abelian surfaces containing no absolutely irreducible curves of low genus

Cites Work

• Construction of rational surfaces yielding good codes
• Geometric construction of some families of two-class and three-class association schemes and codes from nondegenerate and degenerate Hermitian varieties
• Error-correcting codes from higher-dimensional varieties
• Codes defined by forms of degree 2 on Hermitian surfaces and Sørensen's conjecture
• The Jacobian and formal group of a curve of genus 2 over an arbitrary ground field
• Formal groups in genus two.
• Algebraic geometry codes from higher dimensional varieties
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