On the Existence of Aperiodic Perfect Maps for \(2 \times 2\) Windows

Abstract

An aperiodic perfect map (APM) is an array with the property that each possible array of certain size, called a window, arises exactly once as a subarray in the array. In this article, we give some constructions which imply a complete answer for the existence of APMs with \(2 \times 2\) windows for any alphabet size.