Analysis And Construction Of Low Correlation Sequence Sets

Sequences with low correlation play a very important role in cryptography, code-division multiple access (CDMA) communication system etc. Correlation function in-cludesautocorrelationfunctionandcross-correlationfunction. Indifferentapplicationdo-mains, therequirementsonautocorrelationandcross-correlationarealsodifferent. There-fore, it is important to design sequences which meet the communication requirements.This paper analyzes the research background, research status, as well as major re-search methods of low-correlation sequence sets.On this basis, the paper focuses on the equivalent relationship among PN function,theperfectsequencesandcyclicHadamardmatrix. Also, thepapergivesanewequivalentcharacterization of cyclic Hadamard matrix of order4t(t>1), analyzing the run featureswhen its row vectors are regarded as perfect sequences. Then, we get some necessaryconditions about the existence of cyclic Hadamard matrix.At last, we investigate how to construct new low-correlation zone sequence sets.Throughfour-dimensionalinterleavingtechnique,weconstructanoptimal(4N,4M,L,4)-low-correlation zone sequence set.