Towers of Global Function Fields with Asymptotically Many Rational Places and an Improvement on the Gilbert - Varshamov Bound

DOI10.1002/mana.19981950110zbMath0920.11039OpenAlexW2080038939MaRDI QIDQ4224707

Xing, Chaoping, Harald Niederreiter

Publication date: 23 March 1999

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.19981950110

zbMATH Keywords

class field towersrational placesglobal function fieldscurves over finite fieldscodesGilbert-Varshamov boundasymptotic measure of \(\mathbb{F}_q\)-rational points

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Bounds on codes (94B65) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) 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 (10)

Algebraic curves with many points over the binary field ⋮ A modular interpretation of BBGS towers ⋮ Hilbert class field towers of function fields over finite fields and lower bounds for \(A(q)\) ⋮ New lower bounds for the Ihara function \(A(q)\) for small primes ⋮ Some effective results on the Tsfasman-Vlăduţ invariants ⋮ On lower bounds for the Ihara constants  and ⋮ Class number one problem for imaginary function fields: the cyclic prime power case ⋮ Curves of every genus with many points. I: Abelian and toric families. ⋮ Coverings of curves with asymptotically many rational points ⋮ A note on tamely ramified towers of global function fields

Cites Work

• Algebraic function fields and codes
• Algebraic curves over \({\mathbb{F}}_ 2\) with many rational points
• Multiple Kummer extension and the number of prime divisors of degree one in function fields
• On the asymptotic behaviour of some towers of function fields over finite fields
• Tours ramifiées infinies de corps de classes. (Infinite ramified class field towers)
• A tower of Artin-Schreier extensions of function fields attaining the Drinfeld-Vladut bound
• Cyclotomic function fields, Hilbert class fields, and global function fields with many rational places
• Explicit Class Field Theory for Rational Function Fields
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