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

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-Vlǎduţ-Zink lower bound on αq(δ) 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 αqlin for linear codes. © 2007 Society for Industrial and Applied Mathematics.