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01has property X because the set of the first column has the same vector sum as the empty set. Perhaps you meant nonempty sets of columns? I think it's cleaner not to change it though. \$\endgroup\$01has property X:(1) = (0) + (1). If you want to exclude that then you should say that the two sets of columns must be disjoint. \$\endgroup\$2^mcolumn combinations to check property X. If we could somehow devise a "meet in the middle" scheme (see the "subset sum" problem) this could probably reduce that tom * 2^(m/2)... \$\endgroup\$