Integral closures and weight functions over finite fields.

DOI10.1016/S1071-5797(03)00038-8zbMath1085.11059MaRDI QIDQ1414024

Douglas A. Leonard, Pellikaan, Ruud

Publication date: 19 November 2003

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

zbMATH Keywords

NormalizationWeight functionAG codesIntegral closureTowers of function fields

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Integral closure of commutative rings and ideals (13B22) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Structure theory for finite fields and commutative rings (number-theoretic aspects) (11T30)

Related Items (4)

Integral Closure ⋮ Open Problems in Commutative Ring Theory ⋮ On the \(q\)th power algorithm ⋮ Normalization of rings

Uses Software

• QthPower

Cites Work

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• On the structure of order domains
• On the integration of algebraic functions
• Efficient computation of zero-dimensional Gröbner bases by change of ordering
• On the asymptotic behaviour of some towers of function fields over finite fields
• A tower of Artin-Schreier extensions of function fields attaining the Drinfeld-Vladut bound
• A simple approach for construction of algebraic-geometric codes from affine plane curves
• A low-complexity algorithm for the construction of algebraic-geometric codes better than the Gilbert-Varshamov bound
• Finding the defining functions for one-point algebraic-geometry codes
• Systematic encoding via Grobner bases for a class of algebraic-geometric Goppa codes

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