A branch and cut algorithm for finding the minimum distance of a linear block code

We give a branch-and-cut algorithm for finding the minimum distance of a binary linear error correcting code. We give two integer programming (IP) models and study the convex hull of the single constraint relaxation of these IP models. We use the new inequalities as cuts in a branch-and-cut scheme. Finally, we report computational results based on low density parity check (LDPC) codes that demonstrate the effectiveness of our cuts.