The Design And Application Research On New Pseudo-Random Sequences

Pseudo-random sequences are widely used in secret communication,spread spectrum communication system,pseudo-random code ranging,delay measurement,radar navigation and signal synchronization currently.The main indicators that measure randomness properties of a sequence are period,balance,linear complexity and autocorrelation properties.An important application of pseudo-random sequences is used to define cyclic codes.And the minimal polynomial of the defining sequence is used as the generator polynomial of cyclic codes.So in order to obtain the generator polynomial of cyclic code,we need only to find the minimal polynomial of the defining sequence of the code.In this paper,based on the idea of cyclotomic,we construct a class of two-prime Whiteman generalized sequence of order 6 over the field GF(2),and consider the autocorrelation of it.Then we extend one case of the above sequences to the finite field GF(q),and use it to define the cyclic code.And we study on the generator polynomial and the minimum Hamming distance of the cyclic code.Main results are as follows:(1)By extending the combination of cyclotomic class in WGCS-II to the general form,we obtain a class of Whiteman generalized sequence of order 6 over the field GF(2).In this paper,we mainly consider the autocorrelation of the sequence,and give the distribution of the autocorrelation value.(2)This paper extends one case of the above sequence to the finite field GF(q),and use it to define the new cyclic code.(3)It gives the concrete expression of the generator polynomial of the cyclic code in different cases,and calculates the exact value or lower bound of the minimum Hamming distance in different generator polynomial.(4)This paper verifies the theoretical value of the results that we calculate above by using the Magma soft to write the algorithm.And it shows that the theoretical value and experimental value is consistent.