Gray code compression

Abstract

An n-bit (cyclic) Gray code is a (cyclic) sequence of all n-bit strings such that consecutive strings differ in a single bit. We describe an algorithm which for every positive integer n constructs an n-bit cyclic Gray code whose graph of transitions is the d-dimensional hypercube Qd if n = 2 d, or a subgraph of Qd if 2d-1 < n < 2d. This allows to compress sequences that follow this code so that only θ(log log n) bits per n-bit string are needed. The algorithm generates the transitional sequence of the code in a constant amortized time per one transition. © Springer-Verlag Berlin Heidelberg 2009.