The Shift and Add Property of Maximal Length Binary Sequences Using Cyclotomic Polynomials

摘要

A class of binary pseudorandom sequences called maximal length shift register sequences are known to satisfy a shift and add property. That is, if the sequence is shifted by K digits and added to itself, the resulting sequence is the original sequence shifted by R digits. This report presents a method for obtaining the parameter R for a given K and a given maximal length sequence. This procedure makes use of previously published tables and the factorization of cyclotomic polynomials over Galois Field Two. (Author)