两类具有极低自相关性的二元序列

Two classes binary sequences with low autocorrelation

对两类周期分别为N≡2(mod 4)和N≡0(mod 4)的二元序列的自相关性进行了研究。利用周期为N≡1(mod 4)的平衡二元序列的相关性分布特征构造出上述两类序列的自相关性数值的出现频率,给出了上述两类序列的自相关性只存在固定取值且每个取值出现的频率是一定的。结果表明,这两类序列具有良好的周期自相关性,且自相关分布频率是确定的。因此,此类序列能够有效地消除多径效应产生的影响,在密码学和通信领域具有潜在的应用价值。

This paper studied the autocolTelation of two kinds of binary sequences with period N≡2 （mod 4） and N≡0（ mod 4 ）. Utilizing the correlation of balanced sequences with period N≡1 （mod 4） , this article obtained the distribution frequency for the autocorrelation of these binary sequences. Also the autocorrelation of these sequences only existed determined values and the frequency of these values was also determined. The results show that such sequences have good autocorrelation property and distribution frequency of the autocorrelation is determine. Therefore, these sequences can eliminate the effect of multipath, which indicates these sequences have strong potential applications in communication systems and cryptography.