Design Of Several Classes Of Spreading Sequences With Good Properties And Analysis Of Their Linear Complexity

Spreading sequences play a key role in spreading spectrum communication systems. The performance of spreading sequences employed directly influences the performance and capacity of the corresponding spreading spectrum communication systems. There are mainly two kinds of spreading sequences, i.e., the direct spreading sequences and frequency hopping sequences. The correlation properties of the spreading sequences employed are the important criterion of the performance of spreading spectrum communication systems. On the other hand, the linear complexity of the sequences is the main measure of the security of the communication systems. In this thesis, we give a deep study on spreading sequences, and then construct some spreading sequences with good performance. Moreover, we derive at the linear complexity of some spreading sequences.Two new families of p-ary sequences of period pn-1are constructed for odd n=21+1=(2m+1)e and even n=21=2me, respectively. It is shown that, for a given integer p with1≤p≤m, the proposed sequence families both have maximum correlation magnitude1+p(n+2(P-1)e+2)/2; family size (pn-1)p(p-1)"+1, and maximum linear span n(n+3).Two classes of frequency hopping sequences are proposed based on the d-form functions with ideal autocorrelation properties in this thesis. Using the ideal autocorrelation properties of the d-form functions, we calculate the Hamming correlation values of the new sequences and prove that the proposed frequency hopping sequences have optimal Hamming correlation values. Using the HG functions, we can obtain two families of frequency hopping sequences with large linear complexity.By extending the construction of Ding et al based on the perfect nonlinear functions, multiple frequency hopping sequences are constructed using a perfect nonlinear function, and these sequences are proved theoretically to have optimal Hamming auto-and cross-correlation properties.A new generalized cyclotomy with respect to Zp" is presented and the properties of the corresponding generalized cyclotomic numbers are investigated. Based on the new generalized cyclotomy, three classes of frequency hopping sequences are constructed. Using some basic properties of the new generalized cyclotomic numbers, the Hamming autocorrelation properties are derived. The results show that the proposed three classes of frequency hopping sequences all have optimal Hamming autocorrelation values. Besides, these constructions give new parameters.A new frequency hopping sequence set is constructed based on Whiteman's generalized cyclotomy. Based on some properties of Whiteman's generalized cyclotomic numbers, the proposed frequency hopping sequences'Hamming correlation distribution is determined completely and the average Hamming auto-and cross-correlation of the sequence set are calculated. It is shown that the frequency hopping sequence set is optimal with respect to the average Hamming correlation bound.Based on power residue module p, a frequency hopping sequence family with length of sequences being p2and family size (p-1)2is constructed. It is shown that the average Hamming autocorrelation of the new frequency hopping sequence family is0, and the average Hamming crosscorrelation is1. The family is optimal with respect to the average Hamming correlation bound.Cyclotomy has important applications in cryptography, coding theory and pseudo-random sequence design. A class of optimal frequency hopping sequences based on the cyclotomy of Fp was constructed by Chung and Yang (called as Chung-Yang sequences). We determine the linear complexity and minimum polynomial of the Chung-Yang sequences over a prime field. It is shown that these sequences have large linear complexity. By modifying these sequences, another frequency hopping sequence set is obtained. The modified sequences have same Hamming autocorrelation properties, but have larger linear complexity.We introduce Ding's generalized cyclotomic sequences of order4and length p". We determine the linear complexity and autocorrelation of these sequences. It is shown that the minimum and maximal linear complexity of these sequences take (p"+1)/2and p" respectively. Meanwhile, we determine the linear complexity and minimum polynomial of the q-axy Ding's generalized cyclotomic sequences of order q and length p". The results show that these sequences also have large linear complexity.