Sets of disjoint snakes based on a Reed-Muller code and covering the hypercube

Abstract

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 .

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