Flag codes generalize constant dimension codes by considering sequences of nested subspaces with prescribed dimensions as codewords. A comprehensive construction, which unites cyclic orbit flag codes, yields two families of flag codes on $\mathbb{F}^n_q$ (where $n=sk+h$ with $s\geq 2$ and $0\leq h < k$): optimum distance flag codes of the longest possible type vector $(1, 2, \ldots, k, n-k, \ldots, n-1)$ and flag codes with longer type vectors $(1, 2, \ldots, k+h, 2k+h, \ldots, (s-2)k+h, n-k, \ldots, n-1)$. These flag codes achieve the same cardinality $\sum^{s-1}_{i=1}q^{ik+h}+1$.

翻译：旗码通过将具有指定维度的嵌套子空间序列视为码字，推广了常维码。一种统一循环轨道旗码的综合构造方法，在 $\mathbb{F}^n_q$ 上（其中 $n=sk+h$，$s\geq 2$ 且 $0\leq h < k$）生成了两类旗码：具有最长可能类型向量 $(1, 2, \ldots, k, n-k, \ldots, n-1)$ 的最优距离旗码，以及具有更长类型向量 $(1, 2, \ldots, k+h, 2k+h, \ldots, (s-2)k+h, n-k, \ldots, n-1)$ 的旗码。这些旗码均达到相同的基数 $\sum^{s-1}_{i=1}q^{ik+h}+1$。