Let $P$ be a partial order on $[n] = \{1,2,\ldots,n\}$, $\mathbb{F}_{q}^n$ be the linear space of $n$-tuples over a finite field $\mathbb{F}_{q}$ and $w$ be a weight on $\mathbb{F}_{q}$. In this paper, we consider metrics on $\mathbb{F}_{q}^n$ induced by chain orders $P$ over $[n]$ and weights $w$ over $\mathbb{F}_q$, and we determine the cardinality of all optimal anticodes and completely classify them. Moreover, we determine all diameter perfect codes for a set of relevant instances on the aforementioned metric spaces.
翻译：$[$] = $1,2,\ldots,n ⁇ $, $\mathbb{F ⁇ q ⁇ n$, 是一个有限字段的线性空间为n$tuples $\mathbb{F ⁇ q} 美元和 $w$为 $mathbb{F ⁇ q} 的重量。在本文中,我们考虑了由链性订单引起的$mathbb{F ⁇ q}$1,2,\ldots,n ⁇ n$, $mathb{F ⁇ q$, 美元为$\mathb{F ⁇ q$ 美元,我们确定了所有最佳反码的基点,并将其完全分类。此外,我们确定了上述标准空间上一系列相关实例的所有直径完美代码。
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