%0 Journal Article %T On the structure of dense triangle-free binary matroids %A Rutger Campbell %A Jim Geelen %A Peter Nelson %J Mathematics %D 2015 %I arXiv %X We prove, by means of an exact structural description, that every simple triangle-free binary matroid $M$ with $|M| > \tfrac{33}{128}2^{r(M)}$ has critical number at most $2$. %U http://arxiv.org/abs/1504.00040v2