Further improvements on asymptotic bounds for codes using distinguished divisors

Abstract

For a prime power q, let α q be the standard function in the asymptotic theory of codes, that is, α q ( 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 α q ( 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.