On the geometry of Hermitian one-point codes

DOI10.1016/j.jalgebra.2013.08.038zbMath1343.94099arXiv1203.3162OpenAlexW2963180842MaRDI QIDQ405882

Edoardo Ballico, Alberto Ravagnani

Publication date: 8 September 2014

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1203.3162

zbMATH Keywords

Hermitian curveGoppa codeminimum-weight codewordone-point code

Mathematics Subject Classification ID

Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Curves over finite and local fields (11G20) Divisors, linear systems, invertible sheaves (14C20)

Related Items (11)

A comparison between Suzuki invariant code and one-point Hermitian code ⋮ Higher distances for constant dimensions codes: the case of osculating spaces to a Veronese variety ⋮ Hermitian-lifted codes ⋮ Hermitian codes from higher degree places ⋮ The dual geometry of Hermitian two-point codes ⋮ Rational points on cubic surfaces and AG codes from the norm-trace curve ⋮ Minimum-weight codewords of the Hermitian codes are supported on complete intersections ⋮ Lower bounds on the minimum distance in Hermitian one-point differential codes ⋮ On the small-weight codewords of some Hermitian codes ⋮ Hermitian codes and complete intersections ⋮ Dependent subsets of embedded projective varieties

Cites Work

• Hermitian codes from higher degree places
• The dual minimum distance of arbitrary-dimensional algebraic-geometric codes
• Differential approach for the study of duals of algebraic-geometric codes on surfaces
• A zero-dimensional approach to Hermitian codes
• Computing symmetric rank for symmetric tensors
• List decoding of Hermitian codes using Gröbner bases
• Equality of geometric Goppa codes and equivalence of divisors
• Algebraic Function Fields and Codes
• Decoding of Hermitian codes: the key equation and efficient error evaluation
• Improved geometric Goppa codes. I. Basic theory
• Improved Two-Point Codes on Hermitian Curves
• Algebraic Soft-Decision Decoding of Hermitian Codes
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