SIAM Journal on Discrete Mathematics, Volume 35, Issue 3, Page 1688-1705, January 2021.
We show that for any regular matroid on m elements and $\alpha \geq 1$, the number of $\alpha$-minimum circuits, or circuits whose size is at most an $\alpha$-multiple of the minimum size of a circuit in the matroid, is bounded by $m^{O(\alpha^2)}.$ This generalizes a result of Karger for the number of $\alpha$-minimum cuts in a graph. As a consequence, we obtain similar bounds on the number of $\alpha$-shortest vectors in totally unimodular lattices and on the number of $\alpha$-minimum weight code words in regular codes.

中文翻译：

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关于规则拟阵中的电路数（与格和码的连接）

SIAM Journal on Discrete Mathematics，第 35 卷，第 3 期，第 1688-1705 页，2021 年 1 月
。或大小至多是拟阵中电路最小大小的 $\alpha$ 倍数的电路，以 $m^{O(\alpha^2)} 为界。图中 $\alpha$-最小切割的数量。因此，我们在完全单模格子中 $\alpha$-最短向量的数量和常规代码中 $\alpha$-最小权重码字的数量上获得了类似的界限。