IMPROVED ASYMPTOTIC BOUNDS FOR CODES USING DISTINGUISHED DIVISORS OF GLOBAL FUNCTION FIELDS

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-Vladu...

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Bibliographic Details
Published in:SIAM journal on discrete mathematics 2007-01, Vol.21 (4), p.865-899
Main Authors: NIEDERREITER, Harald, OZBUDAK, Ferruh
Format: Article
Language:English
Subjects:
Algebra
Applied mathematics
Codes
Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Laboratories
Linear codes
Mathematics
Sciences and techniques of general use
Valuation
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Summary: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 Özbudak, 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 $\alpha_q^{\rm lin}$ for linear codes.
ISSN:0895-4801
1095-7146
DOI:10.1137/060674478