二值序列偶及其在低相关区序列偶集中的应用

Two-level autocorrelation sequence pairs and their application in low correlation zone sequence pair sets

利用差集偶与二值序列偶的等价关系,证明了异相自相关值为-1的二值序列偶等价对应的差集偶存在的必要条件,并结合特征多项式法构造出(3+2d,2,2+d,2,1)型和(6λ-5,3λ-1,2λ-1,λ+1,λ)型几类差集偶。由该差集偶获得的二值序列偶可应用于低相关区序列偶集的构造,即通过对二值序列偶的循环移位变换构造出低相关值为-1,低相关区长为移位长度Lcz,序列偶数量小于最大低相关区长度N-1与移位长度Lcz之比的最大整数的低相关区序列偶集。

According to the equivalence relation between DSP （difference set pair） and BSPT （binary twolevel autocorrelation sequence pair）, the necessary condition of the existence of DSP corresponding to related BSPT with out-phase autocorrelation value of --1 is put forward and proved, and combining with the characteristic polynomial, the difference set pairs with the parameters of （3 ＋ 2d, 2,2 ＋ d, 2,1 ） and （6λ- 5,3λ-- 1,2λ- 1, 2λ＋,λ） are constructed. By the aid of cyclic shift transform, the related BSPT with out-phase autocorrelation value of -1 can be applied to construct LCZ （low correlation zone） sequence pair sets with correlation function values of -1, in which the LCZ length equals to shift length Lcz, and the number of sequence pairs M is not greater than the maximum integer of the ratio of the maximal LCZ length （N-1） to shift length Lcz.