用整体函数域的区别因子改进码的渐近界
Improved asymptotic bounds for codes using distinguished divisors of global function fields
摘要：
对于素数幂$q$，设$α_q$是码的渐近理论中的标准函数，即$α_q(δ)$是$q$ -元码对给定的渐近相对最小距离$δ$所能达到的最大渐近信息率.近年来，Elkies，Xing，Niederreiter和Özbudak改进了$α_q(δ)$上的Tsfasman-Vllaughduprik-Zink下界.在本文中，我们显示进一步的改进，这些边界上使用的区别因子的整体函数字段。我们还显示了相应的函数$α_q^{\rm lin}$的线性码的改进的下界。
英文摘要：
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. We also show improved lower bounds on the corresponding function $α_q^{\rm lin}$ for linear codes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
