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In the 1970s and 1980s, searches performed by L. Carter, C. Lam, L. Thiel,and S. Swiercz showed that projective planes of order ten with weight 16codewords do not exist. These searches required highly specialized andoptimized computer programs and required about 2,000 hours of computing time onmainframe and supermini computers. In 2011, these searches were verified by D.Roy using an optimized C program and 16,000 hours on a cluster of desktopmachines. We performed a verification of these searches by reducing the problemto the Boolean satisfiability problem (SAT). Our verification uses thecube-and-conquer SAT solving paradigm, symmetry breaking techniques using thecomputer algebra system Maple, and a result of Carter that there are tennonisomorphic cases to check. Our searches completed in about 30 hours on adesktop machine and produced nonexistence proofs of about 1 terabyte in theDRAT (deletion resolution asymmetric tautology) format.

Unsatisfiability Proofs for Weight 16 Codewords in Lam's Problem