Algebraic geometry codes over abelian surfaces containing no absolutely irreducible curves of low genus

DOI10.1016/j.ffa.2020.101791zbMath1456.14056arXiv1904.08227OpenAlexW3117343302MaRDI QIDQ1995221

Elena Berardini, Marc Perret, Yves Aubry, Fabien Herbaut

Publication date: 19 February 2021

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.08227

zbMATH Keywords

finite fieldsabelian surfacesAG codesWeil restrictions

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) Algebraic theory of abelian varieties (14K05)

Related Items

Bounds on the minimum distance of algebraic geometry codes defined over some families of surfaces ⋮ Toward good families of codes from towers of surfaces ⋮ Weil polynomials of abelian varieties over finite fields with many rational points ⋮ Defects of codes from higher dimensional algebraic varieties

Cites Work

• Construction of rational surfaces yielding good codes
• Principally polarizable isogeny classes of Abelian surfaces over finite fields
• Jacobians in isogeny classes of abelian surfaces over finite fields
• Linear codes and modular curves
• Algebraic geometric codes on minimal Hirzebruch surfaces
• Error-correcting codes on low rank surfaces
• Modular curves, Shimura curves, and Goppa codes, better than Varshamov-Gilbert bound
• Codes from Surfaces with Small Picard Number
• Codes from Jacobian surfaces
• Toric Surface Codes and Minkowski Sums
• Abelian varieties over finite fields
• Varieties Defined by Quadratic Equations
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