On the \(q\)th power algorithm

DOI10.1016/j.ffa.2008.06.005zbMath1153.14022OpenAlexW2071056714MaRDI QIDQ958619

Xiaochun Hu, Hiren Maharaj

Publication date: 5 December 2008

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

Full work available at URL: https://doi.org/10.1016/j.ffa.2008.06.005

zbMATH Keywords

algebraic-geometric codesRiemann-Roch spacesintegral closureexplicit bases

Mathematics Subject Classification ID

Integral closure of commutative rings and ideals (13B22) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Algebraic number theory computations (11Y40) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Cites Work

• Algebraic function fields and codes
• On the asymptotic behaviour of some towers of function fields over finite fields
• On lattice reduction for polynomial matrices
• Integral closures and weight functions over finite fields.
• A tower of Artin-Schreier extensions of function fields attaining the Drinfeld-Vladut bound
• 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
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