Finding a basis of a linear system with pairwise distinct discrete valuations on an algebraic curve

DOI10.1006/jsco.2000.0372zbMath0966.14042OpenAlexW1998899281MaRDI QIDQ1587232

Ryutaroh Matsumoto, Shinji Miura

Publication date: 20 February 2001

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jsco.2000.0372

zbMATH Keywords

Gröbner basisalgebraic geometry codeaffine algebraic curveRiemann-Roch spaceideal quotientWeierstraß semigroupplace at infinity

Mathematics Subject Classification ID

Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Computational aspects of algebraic curves (14Q05) Valuations and their generalizations for commutative rings (13A18) Divisors, linear systems, invertible sheaves (14C20) Riemann surfaces; Weierstrass points; gap sequences (14H55)

Related Items (5)

Generalization of the Lee-O'Sullivan list decoding for one-point AG codes ⋮ Computational aspects of retrieving a representation of an algebraic geometry code ⋮ Geometric and Computational Approach to Classical and Quantum Secret Sharing ⋮ List decoding algorithm based on voting in Gröbner bases for general one-point AG codes ⋮ Computing Riemann-Roch spaces in algebraic function fields and related topics.

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