Ding-Helleseth-Martinsen序列的交织结构和自相关分布

Interleaved structure and autocorrelation distribution of Ding-Helleseth-Martinsen sequences

Ding-Helleseth-Martinsen序列是基于中国剩余定理和经典四阶分圆所构造的两类周期为2p的二元序列,其中p为素数且p≡5 (mod 8)。本文通过比较分析该序列和一般交织序列的支撑集的代数特征,证明了其实际上具有p×2交织结构,即可以由两条经典四阶分圆序列利用交织方法生成。在此基础上利用交织序列的自相关公式和经典四阶分圆序列的相关函数值,计算得到所有Ding-Helleseth-Martinsen序列的精确自相关分布。

Ding-Helleseth-Martinsen sequences are two classes of binary sequences of period 2p constructed based on Chinese Residual Theorem and the classical cyclotomy of order four, where p is prime and p≡5(mod 8). By comparing the algebraic characteristics of the support sets of these sequences with those of the general interleaved sequences, it is proved that these sequences actually have a p×2 interleaved structure, i.e. they can be generated by interleaving two classical cyclotomic sequences of order four. On this basis, the accurate autocorrelation distributions of all Ding-Helleseth-Martinsen sequences are determined by using the autocorrelation formula of interleaved sequences and the known correlation function values of the classical cyclotomic sequences of order four.