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

2006/11/09 by Harald Niederreiter, Ferruh Özbudak, Niederreiter, Harald +1
Computer Science · Engineering · #11R58 #11T71 #14G50 #94B27 #94B65 #Algebraic Geometry (math.AG) #Coding theory and cryptography #Error Correcting Code Techniques #FOS: Mathematics #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.math/0611260

openalex publication_date 2006/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a prime power q, let αq be the standard function in the asymptotic theory of codes, that is, αq(δ) is the largest asymptotic information rate that can be achieved for a given asymptotic relative minimum distance δ of q-ary codes. In recent years the Tsfasman-Vlăduţ-Zink lower bound on αq(δ) was improved by Elkies, Xing, and Niederreiter and Özbudak. 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 αq\rm lin for linear codes.

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