Further improvements on the designed minimum distance of algebraic geometry codes

DOI10.1016/j.jpaa.2008.05.003zbMath1160.14012OpenAlexW1992003595MaRDI QIDQ952247

Ịhsan Taşkın, Cem Güneri, Henning Stichtenoth

Publication date: 11 November 2008

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jpaa.2008.05.003

zbMATH Keywords

Goppa codesdesigned minimum distance, floor of a divisor

Mathematics Subject Classification ID

Applications to coding theory and cryptography of arithmetic geometry (14G50) Algebraic functions and function fields in algebraic geometry (14H05)

Related Items (6)

New lower bounds for the minimum distance of generalized algebraic geometry codes ⋮ Floor type bound for the minimum distance of generalized algebraic geometric codes ⋮ Hermitian codes from higher degree places ⋮ Coset bounds for algebraic geometric codes ⋮ Lower bounds on the minimum distance in Hermitian one-point differential codes ⋮ Distance bounds for algebraic geometric codes

Uses Software

• Magma

Cites Work

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• Algebraic function fields and codes
• On the floor and the ceiling of a divisor
• On the existence of non-special divisors of degree \(g\) and \(g-1\) in algebraic function fields over \(\mathbb{F}_2\)
• Consecutive Weierstrass gaps and minimum distance of Goppa codes
• The Magma algebra system. I: The user language
• Riemann-Roch spaces of the Hermitian function field with applications to algebraic geometry codes and low-discrepancy sequences
• On Goppa codes and Weierstrass gaps at several points
• The order bound for general algebraic geometric codes
• A generalized floor bound for the minimum distance of geometric Goppa codes
• The minimum distance of codes in an array coming from telescopic semigroups
• Goppa codes with Weierstrass pairs

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