Linear time construction of a compressed Gray code

An n-bit (cyclic) Gray code is a (cyclic) ordering of all n-bit strings such that consecutive strings differ in exactly one bit. We construct an n-bit cyclic Gray code Cn whose graph of transitions is isomorphic to an induced subgraph of the d-dimensional hypercube where d=⌈lgn⌉. This allows to represent Cn so that only Θ(loglogn) bits per n-bit string are needed. We provide an explicit description of an algorithm which generates the transition sequence of Cn in linear time with respect to the output size.