Let l be an odd prime with \(l\equiv 1\pmod 4\), \(N=l^m\) a positive integer, \({\text {ord}}_N(2)=f\), and \(q=2^f\), where \(f=\phi (N)/t\) and \(\phi (\cdot )\) is the Euler’s function. Let \(\{u_i\}=({\text {Tr}}_{q/2}(\omega ^i))_{i=0}^{q-2}\) be a binary sequence of period \(q-1\), where \(\omega \) is a primitive element of a finite field \(\mathbb F_{q}\). In this paper, we obtain two-valued cross correlation distributions between two sequences \(\{u_i\}\) and their \(\frac{q-1}{N}\)-decimation sequences in two cases: \(t=2\) and \(t=4\).

让l是一个奇素数，\(l\equiv 1\pmod 4\)，\(N=l^m\)一个正整数，\({\text {ord}}_N(2)=f\)，和\(q=2^f\)，其中\(f=\phi (N)/t\)和\(\phi (\cdot )\)是欧拉函数。令\(\{u_i\}=({\text {Tr}}_{q/2}(\omega ^i))_{i=0}^{q-2}\)是一个周期的二进制序列\(q-1\)，其中\(\omega \)是有限域\(\mathbb F_{q}\)的原始元素。在本文中，我们获得了两个序列\(\{u_i\}\)和它们的\(\frac{q-1}{N}\)之间的二值互相关分布- 抽取序列在两种情况下：\(t=2\)和\(t=4\)。