标题： 病毒优化算法在寻找极值二元自对偶码问题中的应用 显示英文标题

标题： An Application of the Virus Optimization Algorithm to the Problem of Finding Extremal Binary Self-Dual Codes

摘要： 在本文中，一种病毒优化算法，作为元启发式优化技术之一，首次被应用于寻找极值二元自对偶码的问题。 我们提出了一些形式为$[I_{36} \ | \ \tau_3(v)],$的生成矩阵，其中$I_{36}$是$36 \times 36$阶单位矩阵，$v$是群矩阵环$M_3(\mathbb{F}_2)G$中的一个元素，而$G$是一个阶数为 12 的有限群，然后我们将它们与病毒优化算法和遗传算法一起使用，以搜索长度为 72 的极值二元自对偶码。 我们得到的结果是，病毒优化算法比遗传算法能找到更多的极值二元自对偶码。 此外，通过使用上述构造以及病毒优化算法，我们能够获得 39 个长度为 72 的 Type I 和 19 个 Type II 码，其重量枚举器中的参数在文献中之前并未被知道。 显示英文摘要

摘要： In this paper, a virus optimization algorithm, which is one of the metaheuristic optimization technique, is employed for the first time to the problem of finding extremal binary self-dual codes. We present a number of generator matrices of the form $[I_{36} \ | \ \tau_3(v)],$ where $I_{36}$ is the $36 \times 36$ identity matrix, $v$ is an element in the group matrix ring $M_3(\mathbb{F}_2)G$ and $G$ is a finite group of order 12, which we then employ together with the the virus optimization algorithm and the genetic algorithm to search for extremal binary self-dual codes of length 72. We obtain that the virus optimization algorithm finds more extremal binary self-dual codes than the genetic algorithm. Moreover, by employing the above mentioned constructions together with the virus optimization algorithm, we are able to obtain 39 Type I and 19 Type II codes of length 72, with parameters in their weight enumerators that were not known in the literature before.