Constructions for perfect maps and pseudorandom arrays

Abstract

A construction of perfect maps, i.e. periodic r*v binary arrays in which each n*m binary matrix appears exactly once, is given. A similar construction leads to arrays in which only the zero n*m matrix does not appear and to a construction in which only a few n*m binary matrices do not appear. A generalization to the nonbinary case is given. The constructions involve an interesting problem in shift-register theory. The solution is given for almost all the case of this problem.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>