Extension of line-splitting operation from graphs to binary matroid

In this paper, we characterize the $n$-line splitting operation of graphs in terms of cycles of respective graphs and then extend this operation to binary matroids. In matroids, we call this operation an element-set splitting. The resulting matroid is called the es-splitting matroid. We characterize circuits of an es-splitting matroid. We also characterize the es-splitting matroid in terms of matrices. Also, we show that if $M$ is a connected binary matroid then the es-splitting matroid $M_X^e$ is also connected.