The complete determination of the minimum distance of two-point codes on a Hermitian curve

DOI10.1007/s10623-005-4599-yzbMath1202.94220OpenAlexW2092150350MaRDI QIDQ851730

Seon Jeong Kim, Masaaki Homma

Publication date: 22 November 2006

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10623-005-4599-y

zbMATH Keywords

Hermitian curveMinimum distanceTwo-point code

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Plane and space curves (14H50) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Curves over finite and local fields (11G20)

Related Items (20)

Two-point AG codes from the Beelen-Montanucci maximal curve ⋮ The order bound for general algebraic geometric codes ⋮ Non-special subsets of the set of points of a curve defined over a finite field ⋮ Algebraic geometric codes on many points from Kummer extensions ⋮ Minimum distance of Hermitian two-point codes ⋮ Coherence of sensing matrices coming from algebraic-geometric codes ⋮ Near weights on higher dimensional varieties ⋮ AG codes and AG quantum codes from the GGS curve ⋮ On the dual minimum distance and minimum weight of codes from a quotient of the Hermitian curve ⋮ Minimum-weight codewords of the Hermitian codes are supported on complete intersections ⋮ Coset bounds for algebraic geometric codes ⋮ Multi-point codes over Kummer extensions ⋮ A zero-dimensional approach to Hermitian codes ⋮ AG codes and AG quantum codes from cyclic extensions of the Suzuki and Ree curves ⋮ Distance bounds for algebraic geometric codes ⋮ On the Weierstrass semigroups of \(n\) points of a smooth curve ⋮ Delta sets for divisors supported in two points ⋮ The second generalized Hamming weight for two-point codes on a Hermitian curve ⋮ Hermitian codes and complete intersections ⋮ Bounds for generalized Hamming weights of general AG codes

Cites Work

• On the index of the Weierstrass semigroup of a pair of points on a curve
• The Weierstrass semigroup of a pair of points on a curve
• The two-point codes on a Hermitian curve with the designed minimum distance
• The two-point codes with the designed distance on a Hermitian curve in even characteristic
• Toward the determination of the minimum distance of two-point codes on a Hermitian curve.
• Weierstrass pairs and minimum distance of Goppa codes
• Goppa codes with Weierstrass pairs

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