Weierstrass semigroups in an asymptotically good tower of function fields

DOI10.1006/ffta.1998.0217zbMath0915.11054OpenAlexW2070874501MaRDI QIDQ1273214

Fernando Torres, Henning Stichtenoth, Pellikaan, Ruud

Publication date: 9 March 1999

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

Full work available at URL: https://doi.org/10.1006/ffta.1998.0217

zbMATH Keywords

Weierstrass semigroupasymptotically good tower of function fields

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Arithmetic ground fields for curves (14H25) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Curves over finite and local fields (11G20) Riemann surfaces; Weierstrass points; gap sequences (14H55)

Related Items (6)

On the existence of non-special divisors of degree \(g\) and \(g-1\) in algebraic function fields over \(\mathbb{F}_2\) ⋮ On the constant 𝐷(𝑞) defined by Homma ⋮ Refined analysis of RGHWs of code pairs coming from Garcia-Stichtenoth's second tower ⋮ The correction capability of the Berlekamp-Massey-Sakata algorithm with majority voting ⋮ Bounding the number of \(\mathbb F_q\)-rational places in algebraic function fields using Weierstrass semigroups ⋮ Weierstrass semigroup at \(m+1\) rational points in maximal curves which cannot be covered by the Hermitian curve

Cites Work

• Algebraic function fields and codes
• Linear codes and modular curves
• 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
• Modular curves, Shimura curves, and Goppa codes, better than Varshamov-Gilbert bound
• An explicit construction of a sequence of codes attaining the Tsfasman-Vladut-Zink bound. The first steps
• The minimum distance of codes in an array coming from telescopic semigroups

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