Maximum cellular boolean functions and perfect gray codes

Abstract

I. A Boolean function of n variables, considered as a subset of t he discl'cLe uni t n-cube Bn> is called cellular if each of its connected components is a face of Bn. Hammin g'~ determination of optimal binary single-error-detectin g codes is generalized to a characteri zation of all propel' cellular functions with the greatest possible number of clements . II. An analysis is made of a class of Gray codes (H amiltonian circuits on Bn) with certain special propcrti es, e.g., ad mi tting for O:Sd:Sn a parti tion in to 2n d subpaths eac h formin g a d-c1 imensional face of Bn.