Delta sets for divisors supported in two points

DOI10.1016/j.ffa.2012.06.005zbMath1279.94150OpenAlexW2085928786MaRDI QIDQ714449

Iwan M. Duursma, Seungkook Park

Publication date: 11 October 2012

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

Full work available at URL: https://doi.org/10.1016/j.ffa.2012.06.005

zbMATH Keywords

Hermitian curvedelta setsSuzuki curvelinear secret-sharing schemealgebraic geometric codeminimum distance boundorder boundgeometric Goppa code

Mathematics Subject Classification ID

Bounds on codes (94B65) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Applications to coding theory and cryptography of arithmetic geometry (14G50) Authentication, digital signatures and secret sharing (94A62)

Related Items (11)

Suzuki-invariant codes from the Suzuki curve ⋮ Weierstrass semigroup and pure gaps at several points on the \(GK\) curve ⋮ Generalized Weierstrass semigroups and Riemann-Roch spaces for certain curves with separated variables ⋮ On Weierstrass gaps at several points ⋮ Generalized Weierstrass semigroups at several points on certain maximal curves which cannot be covered by the Hermitian curve ⋮ On Weierstrass semigroup at \(m\) points on curves of the form \(f(y)=g(x)\) ⋮ Embedding Suzuki curves in \(\mathbb P^4\) ⋮ Triples of rational points on the Hermitian curve and their Weierstrass semigroups ⋮ On the Zeta function and the automorphism group of the generalized Suzuki curve ⋮ Weierstrass semigroup at \(m+1\) rational points in maximal curves which cannot be covered by the Hermitian curve ⋮ Matrix theory for minimal trellises

Cites Work

• Distance bounds for algebraic geometric codes
• Coset bounds for algebraic geometric codes
• The complete determination of the minimum distance of two-point codes on a Hermitian curve
• Riemann-Roch spaces of the Hermitian function field with applications to algebraic geometry codes and low-discrepancy sequences
• On the index of the Weierstrass semigroup of a pair of points on a curve
• Group codes on certain algebraic curves with many rational points
• The order bound for general algebraic geometric codes
• A generalized floor bound for the minimum distance of geometric Goppa codes
• A generalization of the Weierstrass semigroup
• Minimum distance of Hermitian two-point codes
• An Extension of the Order Bound for AG Codes
• Improved Two-Point Codes on Hermitian Curves
• Quotient curves of the Suzuki curve
• Weierstrass pairs and minimum distance of Goppa codes

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