Pseudonoise sequences based on algebraic feedback shift registers

Over the past half century, various statistical properties of pseudorandom sequences have played important roles in a variety of applications. Among these properties are Golomb´s randomness conditions: (R1) balance, (R2) run property, and (R3) ideal autocorrelations, as well as the closely related properties (R4) shift and add, and (R5) de Bruin (uniform distribution of subblocks). The purpose of this paper is to describe the relationships among these conditions, and to introduce a new method for generating sequences with all these properties, using algebraic feedback shift registers.