Representation of Symmetric Shift Registers

TL;DR

A new approach is given where the symmetric shift registers are represented by associated systems of nonlinear difference equations, which clarifies the underlying structures and makes it easier to determine the minimal periods of the sequences generated by the symmetric shift registers.

Abstract

The objective of this work is to establish a mathematical framework for the study of symmetric shift registers over the field GF(2). The present paper gives a new approach where the symmetric shift registers are represented by associated systems of nonlinear difference equations. Arithmetical progressions will play a central part. This approach clarifies the underlying structures and makes it easier to determine the minimal periods of the sequences generated by the symmetric shift registers. Key words: Shift registers, nonlinear difference equations, periods, arithmetical progressions, GF(2).