Removing circuits in 3-connected binary matroids

For a kk-connected graph or matroid MM, where kk is a fixed positive integer, we say that a subset XX of E(M)E(M) is kk-removable   provided M∖XM∖X is kk-connected. In this paper, we obtain a sharp condition on the size of a 3-connected binary matroid to have a 3-removable circuit.