An explicit tower of function fields over cubic finite fields and Zink’s lower bound

DOI10.1515/crll.2005.2005.589.159zbMath1159.11046OpenAlexW2019701198MaRDI QIDQ5713253

Arnaldo Garcia, Henning Stichtenoth, Juscelino Bezerra

Publication date: 13 December 2005

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/crll.2005.2005.589.159

zbMATH Keywords

congruence function fieldsrational placesgenusZink's boundTowers of function fieldsArtin--Schreier extensionscubic finite fieldsDrinfeld--Vlăduţ boundlimits of towersHasse--Weil bound.

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Rational points (14G05) Curves over finite and local fields (11G20) Modular and Shimura varieties (14G35)

Related Items (18)

Further improvements on asymptotic bounds for codes using distinguished divisors ⋮ A modular interpretation of various cubic towers ⋮ A simplified proof for the limit of a tower over a cubic finite field ⋮ Curves of every genus with a prescribed number of rational points ⋮ Block transitive codes attaining the Tsfasman-Vladut-Zink bound ⋮ The Hasse-Witt invariant in some towers of function fields over finite fields ⋮ The exact limit of some cubic towers ⋮ A note on subtowers and supertowers of recursive towers of function fields ⋮ Good recursive towers over prime fields exist ⋮ A new tower with good $p$-rank meeting Zink’s bound ⋮ A modular interpretation of BBGS towers ⋮ Asymptotically good towers of function fields with small \(p\)-rank ⋮ A note on a tower by Bassa, Garcia and Stichtenoth ⋮ Semiample Bertini theorems over finite fields ⋮ Constructions and bounds on linear error-block codes ⋮ On improved asymptotic bounds for codes from global function fields ⋮ Asymptotics for the genus and the number of rational places in towers of function fields over a finite field ⋮ Towards a classification of recursive towers of function fields over finite fields

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