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- r = 3;
- n = 2 r + 1;
- init = DiamondMatrix[r];
- matrices = SparseArray[# -> 1, {n, n}] & /@ Position[DiamondMatrix[r - 1, n], 1];
- matrices = Dilation[Normal@#, DiamondMatrix[1]] & /@ matrices;
- vectors = Flatten@*Normal /@ matrices;
- LinearSolve[Transpose[vectors], Flatten[init], Modulus -> 2]
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