Given an integer n, we can construct $2^n$ strings of length n. We can take the first element for each of these strings and create a list. In total 'n' such lists are possible. But now I need to create lists that are the XOR combinations of the n lists created. If n is 3 and abc is the string then I need to calculate a$\oplus$b, a$\oplus$c, c$\oplus$b, a$\oplus$b$\oplus$c. How do I do this for a general n?
Here's the code so far...
n = 4; s = Tuples[{0, 1}, n]; a = Table[s[[i, j]], {j, 1, n}, {i, 1, 2^n}]
a gives the first four indices of all the strings. Now I need to calculate all the XOR combinations possible between these four lists.
Mod[Plus@##, 2] & @@@ Subsets[a, {2, n}]
give what you need? $\endgroup$Mod[Plus@##, 2] & @@@ Subsets[Transpose[s], {2, n}]
? $\endgroup$Mod[Plus @@@ Subsets[Transpose[s], {2, n}], 2]
$\endgroup$