Study On The Pseudorandom Sequences Of K Symbols

Pseudorandom sequences have extensive application in GPS tracking system and radar monitoring,the construction methods and pseudorandom analysis is the main research content of pseudorandom theory.The well-distribution mea-sure,correlation measure,collision and avalanche effect become the key indexes of pseudorandom sequences to determine good or bad,which has important sig-nificance.In this paper we construct large family of pseudorandom sequences of k symbols with length pq by using generalized cyclotomic classes,and study the properties of these sequences.Firstly,we construct large family of pseudorandom sequences of k symbols with length pq by using Whiteman generalized cyclotomic classes.Then,study the well-distribution measure,correlation measure of order 2 and 3,collision and avalanche effect by using the properties of the Chinese remainder theorem,trigonometric sum,exponential sum and character sum.Secondly,we construct large family of pseudorandom sequences of k symbols with length pq by using Ding-Helleseth generalized cyclotomic classes,and study the pseudorandom properties.Lastly,we construct large family of pseudorandom sequences of k symbols with length pq using the residue class ring modulo pq and the methods of discrete logarithm,and study the pseudorandom properties.