Digital transmission protocols transmit signals using binary codes. In order to minimize the effect of errors, protocols often use codewords for signals with the property that $$similar$$ signals use $$similar$$ codewords.

One such code is a list of $2$n n$-$bit strings in which each string $($except the first$)$ differs from the previous one in exactly one bit. Let us call such a list a bit$-$flip list since we go from one string to the next by just flipping one bit.

Consider the following recursive algorithm for listing the n$-$bit strings of one such bit$-$flip list.

$$ If n $=1,$ the list is $0,1.$

$$ If n $>1,$ first take a bit$-$flip list of $($n $1)-$bit strings, and place a $0$ in front of each string. Then, take a second copy of the same bit$-$flip list of $($n $1)-$bit strings, place a $1$ in front of each string, reverse the order of the strings and place it after the first list.