Improved asymptotic bounds for codes using distinguished divisors of global function fields

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Niederreiter H., ÖZBUDAK F.

SIAM JOURNAL ON DISCRETE MATHEMATICS, vol.21, no.4, pp.865-899, 2007 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 21 Issue: 4
  • Publication Date: 2007
  • Doi Number: 10.1137/060674478
  • Journal Name: SIAM JOURNAL ON DISCRETE MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.865-899
  • Middle East Technical University Affiliated: Yes

Abstract

For a prime power q, let alpha(q) be the standard function in the asymptotic theory of codes, that is, alpha(q)(delta) is the largest asymptotic information rate that can be achieved for a given asymptotic relative minimum distance delta of q-ary codes. In recent years the Tsfasman-Vladut-Zink lower bound on alpha(q)(delta) was improved by Elkies, Xing, Niederreiter and Ozbudak, and Maharaj. In this paper we show further improvements on these bounds by using distinguished divisors of global function fields. We also show improved lower bounds on the corresponding function alpha(lin)(q) q for linear codes.