Bounding the number of \(\mathbb F_q\)-rational places in algebraic function fields using Weierstrass semigroups

DOI10.1016/j.jpaa.2008.11.013zbMath1180.14018arXiv0710.4662OpenAlexW1927331544WikidataQ57735091 ScholiaQ57735091MaRDI QIDQ1008764

Olav Geil, Ryutaroh Matsumoto

Publication date: 30 March 2009

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0710.4662

zbMATH Keywords

function fieldWeierstrass semigrouprational placetower of function fields

Mathematics Subject Classification ID

Arithmetic ground fields for curves (14H25) Curves over finite and local fields (11G20) Finite ground fields in algebraic geometry (14G15) Algebraic functions and function fields in algebraic geometry (14H05)

Related Items (9)

Non-special subsets of the set of points of a curve defined over a finite field ⋮ Bounding the number of points on a curve using a generalization of Weierstrass semigroups ⋮ On the Geil-Matsumoto bound and the length of AG codes ⋮ Algebraic Geometry Codes from Castle Curves ⋮ Triples of rational points on the Hermitian curve and their Weierstrass semigroups ⋮ Weierstrass points on Kummer extensions ⋮ Weierstrass semigroup at \(m+1\) rational points in maximal curves which cannot be covered by the Hermitian curve ⋮ Contemporary coding theory. Abstracts from the workshop held March 17--23, 2019 ⋮ NONHOMOGENEOUS PATTERNS ON NUMERICAL SEMIGROUPS

Uses Software

• manYPoints

Cites Work

• Unnamed Item
• Places of degree one in function fields over finite fields
• Weierstrass semigroups in an asymptotically good tower of function fields
• On the asymptotic behaviour of some towers of function fields over finite fields
• Miura conjecture on affine curves
• Weierstrass Points and Curves Over Finite Fields
• Tables of curves with many points
• On the existence of order functions

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