有限域上方程α2 x＋αtrne1（αx）＋x＋trne2（x）＝0的研究

摘要

Families of binary sequences with low correlation have important applications in CDMA communications,and the correlation of two sequences in a family defined by functions over finite fields is associated with the number of solutions to equations over finite fields. Given positive integers e1 ,e2 and n with e1|n1,e2|e1,we study the number of solutions to α2x+αtrne1(αx) +x+trne2(x) =0 over the field F2n,whereα∈F2n. When e1 =e2,the number of solutions to the equation has been used in the construction for families of binary sequences with low correlation,and we propose a method of constructing families of binary sequences with low correlation for the case e1≠e2 . New families of binary sequences have a large number of numbers and low correlation.%低相关二元序列集在CDMA通信系统中有着重要的应用，由有限域上函数定义的序列集中的两条序列的相关值与有限域上方程的解数有关。设3个正整数e1，e2和n满足e1｜n，e2｜e1，α∈F2n，研究方程α2x＋αtrne1（αx）＋x＋trne2（x）＝0在域F2n上的解数。当e1＝e2时，此方程的解数已被用于构造低相关二元序列集，本文中提出一种当e1≠e2时构造低相关二元序列集的方法。新序列集的数目很大，且相关值较低。