Binary group and Chinese postman polyhedra
Mathematical Programming: Series A and B
On the cycle polytope of a binary matroid
Journal of Combinatorial Theory Series B
Integer and combinatorial optimization
Integer and combinatorial optimization
The intractability of computing the minimum distance of a code
IEEE Transactions on Information Theory
Good error-correcting codes based on very sparse matrices
IEEE Transactions on Information Theory
Improved low-density parity-check codes using irregular graphs
IEEE Transactions on Information Theory
Regular and irregular progressive edge-growth tanner graphs
IEEE Transactions on Information Theory
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We give a branch-and-cut algorithm for finding the minimum distance of a binary linear block 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 turbo and low density parity check (LDPC) codes that demonstrate the effectiveness of our cuts. We demonstrate that our IP formulation and specific cuts are efficient tools for determining the minimum distance of moderate size linear block codes, specifically, they are very efficient for LDPC codes, and provide us with an additional tool for solving this important problem.