  In most of the network coding problems with $k$ messages, the existence of
binary network coding solution over $\mathbb{F}_2$ depends on the existence of
adequate sets of $k$-dimensional binary vectors such that each set comprises of
linearly independent vectors. In a given $k \times n$ ($n \geq k$) binary
matrix, there exist ${n}\choose{k}$ binary sub-matrices of size $k \times k$.
Every possible $k \times k$ sub-matrix may be of full rank or singular
depending on the columns present in the matrix. In this work, for full rank
binary matrix $\mathbf{G}$ of size $k \times n$ satisfying certain condition on
minimum Hamming weight, we establish a relation between the number of full rank
sub-matrices of size $k \times k$ and the weight enumerating function of the
error correcting code with $\mathbf{G}$ as the generator matrix. We give an
algorithm to compute the number of full rank $k \times k$ submatrices.
