How to speed up this code(Jordan Normal Form)

Question

I want to calculate the number of unrepeated Jordan canonical forms of n * n matrices consisting of 0 and 1 How to speed up this code

sol4=Flatten[Inactive[Table][Table[x[(i-1) 4+j],{i,1,4},{j,1,4}],Sequence@@Table[{x[i],0,1},{i,1,16}]]//Activate,15];GatherBy[sol4,(JordanDecomposition[#1][[2]])&]//Length 

Answer 1

This took less than 3 minutes on my Quad Core machine:

A = Tuples[{0, 1}, {4, 4}];
data = ParallelMap[(JordanDecomposition[#1][[2]]) &, A]; // AbsoluteTiming // First
DeleteDuplicates[data] // Length

159.48

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