Constructing snake-in-the-box codes and families of such codes covering the hypercube

A snake-in-the-box code (or snake) is a list of binary words of length n such that each word differs from its successor in the list in precisely one bit position. Moreover, any two words in the list differ in at least two positions, unless they are neighbours in the list. The list is considered to be a cyclic list which implies that the \verb+'...