Sets of disjoint snakes based on a Reed-Muller code and covering the hypercube
A snake-in-the-box code (or snake) of word length n is a simple circuit in an n-dimensional cube Q(n) , with the additional property that any two non-neighboring words in the circuit differ in at least two positions. To construct such snakes a straightforward, non-recursive method is developed based on special linear codes with minimum distance 4. An extension of this method is used for the construction of covers of Q(n) consisting of 2(m-1) vertex-disjoint snakes, for 2(m-1) < n <= 2(m). These covers turn out to have a symmetry group of order 2(m).
snake reed-muller code cover snake-in-the-box-code gray code parallel system invariance group