Decoding Perfect Maps

Perfect Maps are two-dimensional arrays in which every possible sub-array of a certain size occurs exactly once. They are a generalisation of the de Bruijn sequences to two dimensions and are of practical significance in certain position location applications. In such applications the decoding problem, i.e. resolving the position of a particular sub-array within a specified Perfect Map, is of great significance. In this paper new constructions for (binary) Perfect Maps and 2k-ary de Bruijn sequences are presented. These construction methods, although not yielding Perfect Maps for new sets of parameters, are significant because the Maps they yield can be efficiently decoded.