A characterization of the bases of line-splitting matroids

In [1] the author extended $n$-line splitting from graphs to binary matroids and characterized the circuits of the result matroid, i.e. line-splitting matroid (es-splitting). In this paper, we characterize dependent, independent and base sets in line-splitting matroid $M_X^e$. Moreover, we determine rank function of $M_X^e$.