Number System Constructions with Block Diagonal Bases

Abstract

This paper deals with number system constructions using block diagonal bases. We show how easy is creating new generalized number systems from the existing ones via homomorphic constructions. We prove that diagonal extensions can always be performed even if the basic blocks are not number systems. As a special case we consider simultaneous systems in the Gaussian ring. We present a searching method and verify by computer that except 43 cases the Gaussian integers are always able to serve as basic blocks for simultaneous number Systems using dense digit sets.