Structural properties of pseudorandom arrays and volumes and their related sequences

The structure of two-and three-dimensional pseudorandom arrays produced by the folding of binary and multiple-valued m-sequences is investigated. This procedure is shown to be related to the process of sequence sampling, and this enables the recursions corresponding to the rows and columns of the arrays to be related to that of the parent m-sequence. These recursions then determine the nature of symmetries which may be apparent in the arrays. It is also demonstrated that pseudorandom volumes can be constructed by folding any one of the three related two-dimensional arrays. The structure of arrays derived from twin-prime pseudorandom sequences is also investigated. Tables of the available binary and multiple-valued PRAs and PRVs are appended.