For a prime power $q$, let $\alpha_q$ be the standard function in theasymptotic theory of codes, that is, $\alpha_q(\delta)$ is the largestasymptotic information rate that can be achieved for a given asymptoticrelative minimum distance $\delta$ of $q$-ary codes. In recent years theTsfasman-Vl\u{a}du\c{t}-Zink lower bound on $\alpha_q(\delta)$ was improved byElkies, Xing, and Niederreiter and \"Ozbudak. In this paper we show furtherimprovements on these bounds by using distinguished divisors of global functionfields. We also show improved lower bounds on the corresponding function$\alpha_q^{\rm lin}$ for linear codes.
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