随机拟阿贝尔码的保序性
Thresholds of Random Quasi-Abelian Codes
摘要：
对于速率为$r$的随机准阿贝尔码，证明了GV界是一个阈值点：如果$r$小于在$δ$处的GV界，则随机码的相对距离大于$δ$的概率几乎为1;反之，如果$r$大于在$δ$处的GV界，则概率几乎为0。因此，存在许多渐近好的准阿贝尔码，其任何参数都达到GV-界。
英文摘要：
For a random quasi-abelian code of rate $r$, it is shown that the GV-bound is a threshold point: if $r$ is less than the GV-bound at $δ$, then the probability of the relative distance of the random code being greater than $δ$ is almost 1; whereas, if $r$ is bigger than the GV-bound at $δ$, then the probability is almost 0. As a consequence, there exist many asymptotically good quasi-abelian codes with any parameters attaining the GV-bound.
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。
