具有四值自相关特性的二元序列的构造

Construction of Binary Sequences with Four-Level Autocorrelation

本文给出了具有四值自相关特性的二元序列的一种构造方法。对于任意给定的素数p和正整数m、n,当m|n时,我们利用周期为pm-1的具有三值自相关特性的二元序列构造了周期为pn-1的具有四值自相关特性的二元序列,给出了新的二元序列的自相关取值及其分布,同时还讨论了这些序列的陪集不变性和线性复杂度等性质。

The construction of a family of binary sequences with four-level autocorrelation is described.Given any prime p and any positive integers m,n（mn）,we construct a family of binary sequences with period pn-1 and four-level autocorrelation based on a binary sequence with period pm-1 and three-level autocorrelation when m｜n.The distribution of the autocorrelation values of these sequences is derived.Some properties such as constant-on-the-coset property and linear span are discussed.