Given an n x n Hadamard matrix H (with n ≥4) and an integer i with 1 ≤i ≤n, returns the Hadamard 3--design corresponding to the ith row of H.
Given an n x n Hadamard matrix H (with n ≥4) and an integer i with 1 ≤i ≤n, returns the Hadamard 3--design corresponding to the ith column of H.
> R := MatrixRing(Integers(), 8); > H := R![1, 1, 1, 1, 1, 1, 1, 1, > 1, 1, 1, 1, -1, -1, -1, -1, > 1, 1, -1, -1, 1, 1, -1, -1, > 1, 1, -1, -1, -1, -1, 1, 1, > 1, -1, 1, -1, 1, -1, -1, 1, > 1, -1, 1, -1, -1, 1, 1, -1, > 1, -1, -1, 1, -1, 1, -1, 1, > 1, -1, -1, 1, 1, -1, 1, -1]; > IsHadamard(H); true > DR := HadamardRowDesign(H, 3); > DR: Maximal; 3-(8, 4, 1) Design with 14 blocks Points: {@ 1, 2, 3, 4, 5, 6, 7, 8 @} Blocks: {1, 2, 5, 6}, {1, 2, 7, 8}, {1, 2, 3, 4}, {1, 4, 5, 7}, {1, 4, 6, 8}, {1, 3, 6, 7}, {1, 3, 5, 8}, {3, 4, 7, 8}, {3, 4, 5, 6}, {5, 6, 7, 8}, {2, 3, 6, 8}, {2, 3, 5, 7}, {2, 4, 5, 8}, {2, 4, 6, 7} > HadamardColumnDesign(H, 8); 3-(8, 4, 1) Design with 14 blocks