Coverings of curves with asymptotically many rational points

Wen Ching W. Li, Hiren Maharaj

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

Ihara defined the quantity A(q), which is the lim sup as g approaches ∞ of the ratio Nq(g)/g, where Nq(g) is the maximum number of rational points a curve of genus g defined over a finite field Fq may have. A(q) is of great relevance for applications to algebraic-geometric codes. It is known that A(q) ≤ q - 1 and equality holds when q is a square. By constructing class field towers with good parameters, in this paper we present improvements of lower bounds of A(q) for q an odd power of a prime.

Original languageEnglish (US)
Pages (from-to)232-256
Number of pages25
JournalJournal of Number Theory
Volume96
Issue number2
DOIs
StatePublished - Oct 1 2002

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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