Minimum distance of Hermitian two-point codes

DOI10.1007/s10623-009-9361-4zbMath1201.94140arXiv0902.0135OpenAlexW2052927612MaRDI QIDQ2638427

Seungkook Park

Publication date: 16 September 2010

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

Full work available at URL: https://arxiv.org/abs/0902.0135

zbMATH Keywords

Hermitian curveMinimum distanceAlgebraic CodesHermitian two-point code

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Bilinear and Hermitian forms (11E39) Applications to coding theory and cryptography of arithmetic geometry (14G50) Arithmetic codes (94B40)

Related Items

Two-point AG codes from the Beelen-Montanucci maximal curve, Non-special subsets of the set of points of a curve defined over a finite field, Coherence of sensing matrices coming from algebraic-geometric codes, Near weights on higher dimensional varieties, On the dual minimum distance and minimum weight of codes from a quotient of the Hermitian curve, The dual geometry of Hermitian two-point codes, Minimum-weight codewords of the Hermitian codes are supported on complete intersections, An approach to the bases of Riemann-Roch spaces, A zero-dimensional approach to Hermitian codes, 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, Hermitian codes and complete intersections, Bounds for generalized Hamming weights of general AG codes

Cites Work

• Unnamed Item
• Unnamed Item
• The complete determination of the minimum distance of two-point codes on a Hermitian curve
• The order bound for general algebraic geometric codes
• 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.
• Near Orders and Codes
• Decoding algebraic-geometric codes up to the designed minimum distance
• Majority coset decoding
• On the minimum distance of cyclic codes
• The minimum distance of codes in an array coming from telescopic semigroups