Improved Asymptotic Bounds for Codes Using Distinguished Divisors of Global Function Fields
Harald Niederreiter, Ferruh Özbudak · SIAM Journal on Discrete Mathematics · 2007
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–Vlăduţ–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.