The Constructions And Property Analysis Of Binary And Quaternary Sequences

Pseudorandom sequences are widely used in spread spectrum com-munication,code division multiple access communication,global positioning systems and cryptography,et al.The design and analysis of pseudorandom sequences are hot research topics in the world all the time.It is valuable to look for stronger mathemat-ical tool to analyze the properties of existing sequences.This dissertation studies the properties and constructions of binary and quaternary sequences.Main contributions of this work are listed as follows:(1)Based on the inverse Gray mapping and interleaving technique,with the binary ideal autocorrelation sequences with period of N?3(mod 4),two classes of quaternary sequences of even period are derived.One class of the quaternary sequence with low autocorrelation property,another one have optimal autocorrelation proper-ty and have a good balance.The cross correlation function of arbitrary four q-ary sequences with the same period are presented.The relationship relation between the odd-period autocorrelation function of the constructed quaternary sequences and the odd-period autocorrelation function of the employed binary sequences is derived by using the deformation of the inverse Gray mapping,and a new class of the quaternary sequence with good odd-period autocorrelation property is derived.(2)Based on the interleaving technique,taking four binary ideal autocorrelation sequences with period of N?3(mod 4)as the column sequences to N × 4 interleave,we obtain three classes of binary interleaved sequences of even period 4N,One class of the binary sequence with low autocorrelation property,the rest of the two classes have optimal autocorrelation property,and it also has good cross correlation property between two types of sequences.(3)Based on the 2k-Hadamard transform of the indirect sum proposed by Carlet,we present the necessary and sufficient conditions for functions are generated by indirect to be 2k-bent function.