There is a set of $n$ $01$-sequences of length $200.$ Every pair of $01$-sequences differ at least at $101$ positions. (For example, the two $01$-sequences of length $6,$ $111100$ and $010001$ differ at four positions, $1$st, $3$rd, $4$th and $6$th positions, counting from the left.) Is it possible that $n \geq 101?