Binary strings

From the 2010 Australian Maths Challenge:

There are sixteen different ways of writing four-digit strings using 1s and 0s. Three of these strings are 1010, 0100 and 1001. These three can be found as substrings of 101001. There is a string of nineteen 1s and 0s which contains all sixteen strings of length 4 exactly once. If this string starts with 1111, what are the last four digits?

Solution

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