Improved Expression for Rank Distribution of Sparse Random Linear Network Coding

Characterization of the rank distribution of a sparse random matrix over a finite field can be decomposed into two subproblems. The first subproblem is the characterization of the probability $p(i,n)$ that an $n$ -dimensional vector is linearly dependent of other $i$ linearly independent $n$ -dimensional vectors. The second subproblem is the characterization of the rank distribution of a spa...