Gray Codes and Paths on the n-Cube

Abstract

Certain problems in coding and in switching theory require a list of distinct binary n-tuples such that each differs from the one preceding it in just one coordinate. Geometrically, such a list corresponds to a path which follows edges of an n-dimensional cube. This paper finds all types of closed paths on cubes with n ≦ 4. For larger n, a process given here will produce large numbers of paths.