Perfect maps

Given positive integers r, s, u, and υ, an (r, s; u, υ) perfect map (PM) is defined to be a periodic r×s binary array in which every u×υ binary array appears exactly once as a periodic subarray. Perfect maps are the natural extension of the de Bruijn sequences to two dimensions. In the paper the existence question for perfect maps is settled by giving constructions for perfect maps for all parameter sets subject to certain simple necessary conditions. Extensive use is made of previously known constructions by finding new conditions which guarantee their repeated application. These conditions are expressed as bounds on the linear complexities of the periodic sequences formed from the rows and columns of perfect maps