For example, given the set {0011, 1001, 0110, 1110}, the number 1011 can be obtained by performing xor between number in the set
0011 xor 0110 xor 1110 = 0101 xor 1110 = 1011
Another example, given the set {0011, 1001, 0110}, the number 0111 is not in the set and cannot be obtained by performing xor between number in the set
0011 xor 1001 = 1010
0011 xor 0110 = 0101
1001 xor 0110 = 1111
0011 xor 1001 xor 0110 = 1010 xor 0110 = 1100
So given a set of number, how to know whether a number not in the set can be obtained by performing xor operation between number in the set ? trying one by one is simply impractical because i had to try whether the number can be obtained by xor-ing 2 number, or xor-ing 3 number, and so on until xor-ing n amount of number where n in the amount of number in the set.
Is there a shortcut to this?