Optimum distance flag codes (ODFCs), as special flag codes, have received a lot of attention due to its application in random network coding. In 2021, Alonso-Gonz\'{a}lez et al. constructed optimal $(n,\mathcal{A})$-ODFC for $\mathcal {A}\subseteq \{1,2,\ldots,k,n-k,\ldots,n-1\}$ with $k\in \mathcal A$ and $k|n$. In this paper, we introduce a new construction of $(n,\mathcal A)_q$-ODFCs by maximum rank-metric codes. It is proved that there is an $(n,\mathcal{A})$-ODFC of size $\frac{q^n-q^{k+r}}{q^k-1}+1$ for any $\mathcal{A}\subseteq\{1,2,\ldots,k,n-k,\ldots,n-1\}$ with $\mathcal A\cap \{k,n-k\}\neq\emptyset$, where $r\equiv n\pmod k$ and $0\leq r<k$. Furthermore, when $k>\frac{q^r-1}{q-1}$, this $(n,\mathcal A)_q$-ODFC is optimal. Specially, when $r=0$, Alonso-Gonz\'{a}lez et al.'s result is also obtained.

翻译：最优距离旗帜码作为一类特殊的旗帜码，因其在随机网络编码中的应用而受到广泛关注。2021年，Alonso-González等人针对满足$k\in \mathcal A$且$k|n$的集合$\mathcal {A}\subseteq \{1,2,\ldots,k,n-k,\ldots,n-1\}$，构造了最优$(n,\mathcal{A})$-ODFC。本文利用极大秩度量码提出$(n,\mathcal A)_q$-ODFC的新构造方法。证明了对任意满足$\mathcal A\cap \{k,n-k\}\neq\emptyset$的集合$\mathcal{A}\subseteq\{1,2,\ldots,k,n-k,\ldots,n-1\}$，存在规模为$\frac{q^n-q^{k+r}}{q^k-1}+1$的$(n,\mathcal{A})$-ODFC，其中$r\equiv n\pmod k$且$0\leq r<k$。进一步地，当$k>\frac{q^r-1}{q-1}$时，该$(n,\mathcal A)_q$-ODFC达到最优。特别地，当$r=0$时，可复现Alonso-González等人的结果。