The es-splitting operation on a [Formula: see text]-connected binary matroid may not preserve the [Formula: see text]-connectedness of the matroid. In this paper, we provide a sufficient condition for a [Formula: see text]-connected binary matroid to yield a [Formula: see text]-connected binary matroid under the es-splitting operation. We derive a splitting lemma for [Formula: see text]-connected binary matroids as an application of this result.

The splitting operation on an n-connected binary matroid may not yield an n-connected binary matroid. In this paper, we characterize n-connected binary matroids which yield n-connected binary matroids by the generalized splitting operation.

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The es-splitting operation on binary matroids is a natural generalization of Slater's <em>n</em>-line splitting operation on graphs. In this paper, we characterize the closure operator of the es-splitting binary matroid M^e_X in terms of the closure operator of the original binary matroid M. We also describe the ats and the hyperplanes of the es-splitting bi- nary matroid M^e_X in terms of the ats and the hyperplanes, respectively of the original binary matroid M.

In general, element splitting operation on a matroid M with ground set E is the operation defined by creating a single element coextension of M by adding an element x that creates a cocircuit with T ⊂ E which is not a cocircuit of M . And then deletion of x from this coextension gives a T -split of M denoted by MT . Note that T -split of M may not preserve the n-connectivity of the matroid M . The present paper defines related notion of element splitting operation for matroids representable over GF (p) which preserves the n-connectivity of the matroid and characterizes circuits, bases and hyperplanes of the resulting matroid. The effect of this operation on Eulerian, bipartite and connected matroids which are representable over GF (p) is also studied.