In this paper, first steps are taken towards characterizing rank-decorated lattices of cyclic flats $\mathcal{Z}(M)$ that belong to matroids M that can be represented over a prescribed finite field ${\mathbb{F}}_q$. Two natural maps from $\mathcal{Z}(M)$ to the lattice of cyclic flats of a minor of M are given. Binary matroids are characterized via their lattice of cyclic flats. It is shown that the lattice of cyclic flats of a simple binary matroid without isthmuses is atomic.

中文翻译：

---

二元拟阵的循环平面

在本文中，迈出了第一步，以表征循环平面的秩装饰格 $\mathcal{ž}（\mathrm{中号}）$属于拟阵M的阵，可以在规定的有限域上表示${\mathbb{F}}_q$。来自的两个自然图$\mathcal{ž}（\mathrm{中号}）$给出了M的次要平面的晶格。二元拟阵阵的特征是其环状平面的晶格。结果表明，没有地峡的简单二元拟阵的环状平面的晶格是原子的。