[math-fun] Re: Path Question

Fred Lunnon writes:

Even if the following were to work, it would hardly qualify as an "explicit" construction: but for what it's worth, suppose we have already to hand a (cyclic) deBruijn sequence S_n in which every binary word of length n occurs as a factor exactly once.

...

Lest this all seem absurdly half-baked, here's an example:

n = 4: 00101101 00001111

n = 5: 00101101 11010100010011 0000011111

A very nice idea! Can it be taken out to infinity? Jim