In this paper, a new search technique based on the virus optimisation algorithm is proposed for calculating the neighbours of binary self-dual codes. The aim of this new technique is to calculate neighbours of self-dual codes without reducing the search field in the search process (this is a known in the literature approach due to the computational time constraint) but still obtaining results in a reasonable time (significantly faster when compared to the standard linear computational search). We employ this new search algorithm to the well-known neighbour method and its extension, the $k^{th}$-range neighbours and search for binary $[72,36,12]$ self-dual codes. In particular, we present six generator matrices of the form $[I_{36} \ | \ \tau_6(v)],$ where $I_{36}$ is the $36 \times 36$ identity matrix, $v$ is an element in the group matrix ring $M_6(\mathbb{F}_2)G$ and $G$ is a finite group of order 6, which we then employ to the proposed algorithm and search for binary $[72,36,12]$ self-dual codes directly over the finite field $\mathbb{F}_2$. We construct 1471 new Type I binary $[72, 36, 12]$ self-dual codes with the rare parameters $\gamma=11, 13, 14, 15, 17, 19, 20, 21, 22, 23, 25, 26, 28, 29, 30, 31, 32$ in their weight enumerators.

中文翻译：

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来自 $M_6(\mathbb{F}_2)G$ 的长度为 72 的新极值二进制自对偶代码 - 通过基于邻域病毒优化算法的混合搜索技术对矩阵环进行分组

本文提出了一种新的基于病毒优化算法的搜索技术，用于计算二进制自对偶码的邻居。这种新技术的目的是在不减少搜索过程中的搜索域的情况下计算自对偶码的邻居（由于计算时间限制，这是文献方法中已知的），但仍然在合理的时间内获得结果（显着与标准线性计算搜索相比更快）。我们将这种新的搜索算法应用于众所周知的邻居方法及其扩展，$k^{th}$-range 邻居并搜索二进制 $[72,36,12]$ 自对偶代码。特别是，我们提出了 $[I_{36} \ | 形式的六个生成器矩阵。\ \tau_6(v)],$ 其中 $I_{36}$ 是 $36 \times 36$ 单位矩阵，$v$ 是群矩阵环 $M_6(\mathbb{F}_2)G$ 中的一个元素，$G$ 是 6 阶有限群，然后我们将其用于所提出的算法并搜索二进制 $[72 ,36,12]$ 直接在有限域 $\mathbb{F}_2$ 上的自对偶码。我们用稀有参数 $\gamma=11, 13, 14, 15, 17, 19, 20, 21, 22, 23, 25, 构造了 1471 个新的 I 型二进制 $[72, 36, 12]$ 自对偶码， 26、28、29、30、31、32$ 的权重枚举器。