Bases of Riemann-Roch spaces from Kummer extensions and algebraic geometry codes

DOI10.1016/j.ffa.2022.102025OpenAlexW4214672410WikidataQ114179455 ScholiaQ114179455MaRDI QIDQ2123312

Yanyan Li

Publication date: 8 April 2022

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ffa.2022.102025

zbMATH Keywords

algebraic geometry codesKummer extensionsRiemann-Roch spaces

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) Algebraic functions and function fields in algebraic geometry (14H05)

Uses Software

• MinT

Cites Work

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• Consecutive Weierstrass gaps and minimum distance of Goppa codes
• On codes from norm-trace curves
• On Kummer covers with many rational points over finite fields.
• 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
• A construction of curves over finite fields
• Algebraic Function Fields and Codes
• Generalized Hermitian Codes Over$hboxGF,(2^r)$
• A note on Hermitian codes over GF(q/sup 2/)
• Weierstrass pairs and minimum distance of Goppa codes
• Goppa codes with Weierstrass pairs

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