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

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2007-01-01

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Niederreiter, Harald
Özbudak, Ferruh

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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.

Subject Keywords

Asymptotic theory of codes, Gilbert-Varshamov bound, Global function fields, Tsfasman-Vladut-Zink bound, Xing bound

URI

https://hdl.handle.net/11511/35109

Journal

SIAM JOURNAL ON DISCRETE MATHEMATICS

DOI

https://doi.org/10.1137/060674478

Collections

Department of Mathematics, Article

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Citation Formats

H. Niederreiter and F. Özbudak, “Improved asymptotic bounds for codes using distinguished divisors of global function fields,” SIAM JOURNAL ON DISCRETE MATHEMATICS, pp. 865–899, 2007, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/35109.