Constructing snake-in-the-box codes and families of such codes covering the hypercube
Loeky Haryanto · Data Archiving and Networked Services (DANS) · 2007
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+'+first word\\verb+'+ is the successor of the \\verb+'+last word\\verb+'+. The two defining rules mentioned above have to be interpreted in cylic sense. There are some methods known to construct such codes. These are all of a recursive nature, i.e. snakes of a certain length $n$ are constructed from snakes of length $m 2,$ our method delivers concrete covers of $Q_n$ with a large symmetry group.