| Pseudo-random sequences are widely used in many areas of cryptography and spreadspectrum communication.In cryptography,pseudo-random sequences used as keystreams need to have high linear complexity,2-adic complexity,etc.In spread-spectrum communication,pseudo-random sequences should have low autocorrelation and cross-correlation to ensure signal transmission quality and multi-user signal separation.Interleaving technique is an important method for designing pseudo-random sequences.It can not only quickly construct more new longer-period sequences applicable to cryptography and communication from known sequences,but also analyze the randomness properties of new sequences based on the randomness properties of known sequences.Thus,the study of interleaving construction and the calculation of pseudo-random properties such as autocorrelation and linear complexity of sequences are of great research significance.This thesis studies the interleaving construction,autocorrelation,and linear complexity of binary sequences,as well as the interleaving structure characteristics of binary sequences,and achieves the following results:(1)Two types of binary interleaved sequences with period 4p are constructed based on Hall’s sextic residue sequences and their modified sequences.By using the autocorrelation and cross-correlation properties of Hall’s sextic residue sequences and their modified sequences,as well as the autocorrelation function formula of binary interleaved sequences,the autocorrelation values of these two types of sequences are determined completely.The results show that both types of sequences have low autocorrelation,and their values are very close to the optimal autocorrelation magnitude.(2)By studying the roots of the sequence polynomials of the two constructed types of binary interleaved sequences in the splitting field of xp-1 over the finite field F2,the linear complexity and minimal polynomial of these two types of sequences are determined.Specifically,the linear complexity of the second type of sequence is 4p-γ with γ∈｛1,2,3,4}.In most cases,the linear complexity of the first type of sequence is 4p.From the perspective of linear complexity,the two types of sequences are both considered good.(3)By studying the inverse mapping of isomorphic mappings from Z4p to Z4 × Zp,the support set in Z4p of each of these three types of sequences with period of 4p based on the Chinese Residue Theorem is divided into four subsets,and the p×4 interleaving structures of these three classes of sequences are obtained.Furthermore,Their structural characteristics of these three types of sequences are analyzed to a certain extent.This study also reveals the intrinsic connection between binary sequences constructed based on the Chinese Residue Theorem and binary sequences constructed using interleaving technique. |
