Constructions Of Binary Sequence Set With Low Correlation And Frequency Hopping Sequence Set

Pseudo-random sequences play a very important role in cryptography, code division multiple access (CDMA) communication systems, coding, radar, sonar etc. There are two spread spectrum techniques of code division multiple access (CDMA) communication systems, i.e., direct sequence spread spectrum (DSSS) technique and frequency hopping spread spectrum (FHSS) technique. The pseudo-random seque-nces used in direct sequence spread spectrum (DSSS) systems are called spreading sequences. The pseudo-random sequences are called frequency hopping sequences when they are used in frequency hopping spread spectrum (FHSS) systems. In code division multiple access (CDMA) communication systems, the correlations of pse-udo-random sequences determine the level of the multiple-access interference and multi-path interference of the corresponding systems, and it influences the performance and capacity of the corresponding systems directly. In this paper, we give a study on two topics related to sequence design, i. e., sequences with low correlation of large set and optimal frequency hopping sequence set.Firstly, a new binary sequences with low correlation of large set are investigated by using the theory of Niho exponents and trace function over finite fields with even characteristic. By studying the cyclic codes of length of2n—1when n=2k>4, and the research on the weight distribution of cyclic codes of Niho exponent done by Li, Zeng, Hu, a new large set of binary sequences with low correlation is obtained. This set has period2n—1, set size23n/2+2n/2and the maximum correlation3·2n/2—1for even n. By using Walsh spectrum, we get the distri-bution of the correlation values of the sequences in the set.Secondly, based on the generalized cyclotomies, optimal frequency-hopping sequence set is investigated. Using the generalized cyclotomy technology on Zv, with odd v which was proposed by Zeng, Cai, Tang and Yang, a construction of frequency hopping sequence set with new parameters is obtained. And the frequency hopping sequence set can be near optimal with respect to the Peng-Fan bound.