AG codes from the second generalization of the GK maximal curve

DOI10.1016/j.disc.2020.111810zbMath1435.14027arXiv1901.08897OpenAlexW2999610468WikidataQ126341995 ScholiaQ126341995MaRDI QIDQ2305924

Maria Montanucci, Vincenzo Pallozzi Lavorante

Publication date: 20 March 2020

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.08897

zbMATH Keywords

algebraic-geometric codesmaximal curvesWeierstrass semigroups

Mathematics Subject Classification ID

Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Special algebraic curves and curves of low genus (14H45) Riemann surfaces; Weierstrass points; gap sequences (14H55) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Related Items

Two-point AG codes from the Beelen-Montanucci maximal curve, AG codes from \(\mathbb{F}_{q^7}\)-rational points of the GK maximal curve, On Kummer extensions with one place at infinity, Generalized Weierstrass semigroups at several points on certain maximal curves which cannot be covered by the Hermitian curve, On certain self-orthogonal AG codes with applications to quantum error-correcting codes, AG codes from the second generalization of the GK maximal curve

Uses Software

• GUAVA

Cites Work

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• A new family of maximal curves over a finite field
• Good and asymptotically good quantum codes derived from algebraic geometry
• The automorphism groups of a family of maximal curves
• AG codes from the second generalization of the GK maximal curve
• Algebraic Function Fields and Codes
• A generalization of the Giulietti–Korchmáros maximal curve
• On Weierstrass points and optimal curves
• A characterization of Hermitian function fields over finite fields.
• Automorphisms of curves and Weierstrass semigroups for Harbater–Katz–Gabber covers
• Systematic encoding via Grobner bases for a class of algebraic-geometric Goppa codes
• The automorphism group of the generalized Giulietti–Korchmáros function field
• GUAVA