标题： 对称移位寄存器的表示 显示英文标题

标题： Representation of Symmetric Shift Registers

摘要： 本文工作的目标是建立一个关于GF(2)域上对称移位寄存器的数学框架。 本文提出了一种新方法，其中对称移位寄存器由相关的非线性差分方程组表示。 算术级数将起到核心作用。 这种方法阐明了潜在的结构，并使得更容易确定由对称移位寄存器生成的序列的最小周期。 关键词：移位寄存器，非线性差分方程，周期，算术级数，GF(2)。 显示英文摘要

摘要： 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).