The Construction Of Several Classes Of Sequences Over Galois Rings And Research On Their Cryptographic Properties

At present,the wide application of sequences involves code division multiple access communication,spread spectrum communication,global positioning system,cryptography,calculation,control and other fields.Among these fields,having good cryptographic properties plays a very important position,and the linear complexity and correlation are two important indicators to evaluate sequences good or bad.For a long time,the sequence structure design research has always been concerned by the international society,to find some new methods to construct the design sequences with good property and to analyse their cryptographic property has much research value.This article mainly researches the structure of several families of sequences on Galois ring and related cryptographic properties.The main results are shown as follows:(1)A map Z from Z2sk to Z2s-1k×Z2s-1k is defined,and a family of cyclic Z2s-1-codes with a lower bound of the minimum Lee distance is constructed by making use of mapping Z and(2s-1+1)-constacyclic codes over Galois rings Z2s.(2)On the basis of the structure of the cyclic Z2s-1-codes which have been constructed,we construct a family of 2s-1-phase sequences with a low correlation.(3)On the basis of the structure of the 2s-1-phase sequences which have been constructed,we construct a family of biphase sequences with a low correlation by making use of the most significant bit mapping.(4)By making use of the permutation on Galois rings,a new family of No sequences over Galois ring Zpe is constructed and the exact lower bound of the linear complexity is given.