可分差集偶与几乎最佳二元序列偶的研究

Divisible Difference Set Pair and Approach for the Study of Almost Perfect Binary Sequence Pair

在雷达、声纳等工程领域中具有良好相关性的序列得到广泛应用.几乎最佳二元序列偶具有良好的自相关性,它的异相自相关函数只有一点不为零.为了进一步研究几乎最佳二元序列偶,提出了一类新的区组设计——可分差集偶,研究了可分差集偶的性质,给出了可分差集偶与几乎最佳二元序列偶的对应关系,应用可分差集偶的性质得到了几乎最佳二元序列偶存在的必要条件.为应用可分差集偶这种区组设计的方法研究几乎最佳二元序列偶提供了理论依据.

Periodic sequences with good correlation properties have important applications in various areas of engineering. Almost perfect binary sequence pair is a kind of periodic correlation signal, which exhibits zero out-of-phase autocorrelation except one value. In order to do further research on almost perfect binary sequence pair, a new block design（divisible difference set pair）is presented. The properties of divisible difference set pair are studied. The equivalent relationship between almost perfect binary sequence pair and the new block design is given. Several admissibility conditions for almost perfect binary sequence pair are presented, which can improve the searching efficiency. Theoretical basis for using divisible difference set pair to study almost perfect binary sequence pair is proved.