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

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

2006-11-09

arxiv.org/abs/math/0611260v1

Mathematics

Algebraic Geometry

Scientific paper

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-Vl\u{a}du\c{t}-Zink lower bound on $\alpha_q(\delta)$ was improved by Elkies, Xing, and Niederreiter and \"Ozbudak. 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.

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