Riemann-Roch spaces of the Hermitian function field with applications to algebraic geometry codes and low-discrepancy sequences

DOI10.1016/j.jpaa.2004.06.010zbMath1087.14024OpenAlexW2014752373MaRDI QIDQ1764820

Hiren Maharaj, Gretchen L. Matthews, Gottlieb Isabel Pirsic

Publication date: 22 February 2005

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.2004.06.010

zbMATH Keywords

divisorsfloor of a divisor

Mathematics Subject Classification ID

Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Applications to coding theory and cryptography of arithmetic geometry (14G50) Well-distributed sequences and other variations (11K36) Algebraic functions and function fields in algebraic geometry (14H05)

Related Items

Bases of Riemann-Roch spaces from Kummer extensions and algebraic geometry codes, The order bound for general algebraic geometric codes, New lower bounds for the minimum distance of generalized algebraic geometry codes, Multi-point codes from the GGS curves, Explicit equations for maximal curves as subcovers of the \(BM\) curve, The dual geometry of Hermitian two-point codes, Isometry-Dual Flags of Many-Point AG Codes, An approach to the bases of Riemann-Roch spaces, Generalized Weierstrass semigroups and Riemann-Roch spaces for certain curves with separated variables, Multi-point codes over Kummer extensions, Pure Weierstrass gaps from a quotient of the Hermitian curve, Further improvements on the designed minimum distance of algebraic geometry codes, Distance bounds for algebraic geometric codes, Weierstrass semigroups and codes from a quotient of the Hermitian curve, Delta sets for divisors supported in two points, A generalized floor bound for the minimum distance of geometric Goppa codes, On the floor and the ceiling of a divisor

Uses Software

• KANT/KASH

Cites Work

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• On Goppa codes and Weierstrass gaps at several points
• Group codes on certain algebraic curves with many rational points
• Geometric reed-solomon codes of length 64 and over 65 over F/sub 8/
• Low-discrepancy sequences obtained from algebraic function fields over finite fields
• Weierstrass pairs and minimum distance of Goppa codes
• Goppa codes with Weierstrass pairs