Study On Constructions Of Binary Sequence Sets With Low Correlation And Sequence Pairs With Three-level Correlation

Correlation function is an important parameter to measure sequence's performance,and se-quence(pairs)with low autocorrelation also have significant applications in communication systems and cryptography.Meanwhile,the design of sequence(pair)sets with low auto-correlation is also an important topic in sequence design.Aiming at the constructions of sequence(pair)sets with low autocorrelation,binary sequence(pair)sets with low autocor-relation,even period quaternary sequences with low autocorrelation and polyphase sequence pairs with low autocorrelation are discussed in this thesis.The main results are as follows.Firstly,after studying binary ideal autocorrelation sequences,a family of low autocorrelation sequences of period N?3(mod 4)is obtained.A new family of binary sequences of peri-od 4N is constructed by interleaving binary ideal autocorrelation sequences and the former sequences of N?3(mod 4),it is shown that the out-of-phase autocorrelation values of new sequences are{0,±4},that is,new sequences have optimal autocorrelation magnitude.The equivalence of interleaved sequences is considered,compared with the known binary sequence families of period 4N with low autocorrelation,new sequence families include one known sequence family and are inequivalent to the other sequence families.Secondly,a family of quaternary sequences of period 2p is obtained by interleaving Tang-Lindner sequences of period p,where p=4f+1=x²+4y²is an prime.The out-of-phase autocorrelation values of new sequences are{2,-2}when x=1,that is,which can meet the bound of autocorrelation for even period quaternary sequences.Compared with the known even period quaternary sequences with low autocorrelation,new sequences provide new ideas to construct low autocorrelation quaternary sequence families,and have the flexible parameter on period.Thirdly,two families of even period binary sequence pairs with low autocorrelation are proposed by finite field theorem and combination design theorem.The first class of binary sequence pairs of period q-1 are constructed by using the quadratic polynomials over finite field,whose have optimal three-level correlation,where q is a power of an odd prime.The second class of binary sequence pairs of period 4p are presented based on interleaved technique,whose have optimal autocorrelation magnitude,where p?3(mod 4)is an prime.Two classes of binary sequence pairs enrich the types of binary sequence pairs,and construction methods reveal new ideas for binary sequence pair design.Fourthly,a class of polyphase sequence pairs is proposed based on cyclotomy theorem,where the maximum out-of-phase correlation magnitude of the sequence pairs is less than3.Then,ternary(quaternary)sequence pairs of odd period with three-level correlation are obtained by using cyclotomic classes of order three and four.The maximum out-of-phase correlation magnitude of two classes of sequence pairs are less than 7^1/2 and 5^1/2 ,respectively.Compared with the known three-level sequence pairs,new polyphase sequence pairs have better performances on the properties of balance and correlation.Fifthly,a class of p-ary sequence pairs of period 2p²is presented based on the properties of Fermat quotient modulo p and interleaved technique,where p is an odd prime,whose the out-of-phase correlation values only include one nonzero element,that is to say,new sequence pairs have almost perfect autocorrelation.There are not plenty of studies on almost perfect polyphase sequence pairs,thus,new sequence pairs expand the space of sequence pairs.Additionally,the construction method of new sequence pairs reveals ideas for the design of almost perfect sequence pairs.