基于两族函数的低相关二元序列集构造

低相关序列集在码分多址(CDMA)扩频通信系统和密码系统中具有极其重要的作用,运用有限域上的函数族能有效地构造相关性较好的序列集.针对n≡2(mod 4)时,本文首次运用阶数为2ⁿ的有限域上的两个二次布尔函数族,构造了2^2n-2个低相关序列集;这里每个序列集包含2ⁿ+1条周期为2ⁿ-1的二元序列,其最大相关值为2^n/2+1+1.这将为通信系统和密码系统提供更多可供选择的序列集.

Construction for Families of Binary Sequences with Low Correlation Based on Two Families of Functions

Families of pseudorandom sequences with low correlation are useful in a wide range of applications,such as code-division multiple access(CDMA) communications and cryptology,and the families with desired correlation can be effectively constructed by using function families over finite fields.In this paper,2^2n-2 families of binary sequences with low correlation are constructed by using two families of Boolean functions over the finite field with 2ⁿ elements,where n≡2(mod 4).There are 2ⁿ+1 binary sequences of period 2ⁿ-1 within each family,and the maximum correlation is 2^n/2+1+1.The proposed construction can provide more families for CDMA communications and cryptology.