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Towers of Global Function Fields with Asymptotically Many Rational Places and an Improvement on the Gilbert ‐ Varshamov Bound
Author(s) -
Niederreiter Harald,
Xing Chaoping
Publication year - 1998
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19981950110
Subject(s) - mathematics , finite field , rational function , class (philosophy) , function (biology) , order (exchange) , field (mathematics) , algebraic number , upper and lower bounds , pure mathematics , discrete mathematics , mathematical analysis , computer science , finance , artificial intelligence , evolutionary biology , economics , biology
We construct infinite class field towers of global function fields with asymptotically many rational places. In this way, we improve on asymptotic bounds of Serre, Perret, Schoof, and Xing. The results can be interpreted equivalently as asymptotic bounds on the number of rational points of smooth algebraic curves over finite fields. As an application, we show an improvement on the Gilbert‐Varshamov bound for linear codes over finite fields of a sufficiently large composite nonsquare order.