In this paper, we present a set covering problem (SCP) formulation to compute the degree of redundancy of linear systems. Computing the degree of redundancy of a linear system allows for the evaluation of the quality of the sensor network. The formulation is equivalent to solving the linear matroid cogirth problem, finding the cardinality of the smallest cocircuit of a matroid. We also discuss existing methods developed to solve the matroid cogirth problem and the SCP. Computational results are provided to validate a branch-and-cut algorithm that addresses the SCP formulation.