两类广义分圆序列的自相关值

Autocorrelation values of two classes of generalized cyclotomic sequences

基于广义分圆理论,构造了一类周期为2p的二元广义分圆序列和一类周期为pq的二元广义分圆序列,利用分圆数和差集理论讨论了这2类序列的自相关函数值。对于周期为2p的二元广义分圆序列,当p≡1(mod8)时,该类序列具有几乎最优的自相关函数值;当p≡3(mod8)时,该类序列的自相关函数值是四值。对于周期为pq的二元广义分圆序列,当(p-1)(q-1)/4是偶数时,该类序列具有几乎最优的自相关函数值;当(p-1)(q-1)/4是奇数时,该类序列的自相关函数值为四值。结果表明,构造的2类二元广义分圆序列都具有低值自相关性质。

A class of generalized cyclotomic binary sequences with period 2p and a class of generalized cyclotomic binary sequences with periods pq are constructed based on generalized cyclotomic theory.The autocorrelation values of two classes of generalized cyclotomic binary sequences with periods 2p and pq are determined by cyclotomic number and different sets.The class of binary sequences with period 2p have almost optimal autocorrelation function values when p≡1(mod8)and 4-value autocorrelation when p≡3(mod8).The class of binary sequences with periods pq have almost optimal autocorrelation function values when(p-1)(q-1)/4 is even and 4-value autocorrelation when(p-1)(q-1)/4 is odd.Results show that the class of sequences with periods pq and 2p in this paper have low-value autocorrelation.