Study On The Properties Of Cyclotomic Sequences With Period 4 P

Pseudo random sequence is a key research object in cryptography.It has been widely used in many fields,such as distance measurement,radar navigation system,code division multiple access system of stream cipher system and spread spectrum communication system.In general,a good pseudo random sequence has large linear complexity and low autocorrelation valuations.This paper mainly constructs binary sequences with low autocorrelation valuation and large linear complexity.Firstly,by cyclotomic numbers,Chinese residual theorem and Gray mapping,this paper constructs two types of the binary sequenceuses with the period 4 p,p ?1?mod 4?.Secondly,by the relation between the autocorrelation function of the binary sequence and its difference function of its support set,this paper gives the four-valued autocorrelation functions of two types of sequences,which is good.Finally,this paper calculates the linear complexity of two types of sequences over the extension field of GF?2?.If p ?5?mod8?,its linear complexity is larger than half of its period,which is a large linear complexity.And,if p ?1?mod8?,it has a large linear complexity.