一类新的不同周期的四值相关二元序列

发布时间：2018-10-08 17:53

【摘要】：低相关序列是一类有着很好代数性质的特殊序列,它被广泛应用于雷达,CDMA通信系统等多个领域.具有相同周期的低相关序列函数已经研究了将近40多年,特别是近些年来m序列的相关分布受到了广泛的关注和研究也有很多很好的成果.从20世纪70年代以来,Trachtenberg, Niho和Helleseth写了很多关于这个方面有影响力的论文.不同周期的低相关序列分布也是相关序列分布的一个重要方面.本文令k为奇数,q = 22k,研究了周期为q - 1的二元m序列u(t)和周期为(q - 1)/3的二元m序列vl(t) = u(dt + l), 0 ≤ l ≤ 2,其中d和s分别满足d = (2kk - 1)s + 1和(22r+ ) ≡1(mod2k + 1)的相关分布情况.我们运用了有限域上二次型理论以及一些代数方程组求解技巧等确定了满足上述条件的相关分布是一个四值分布.当l = 0时,我们得出满足上述条件相关函数的值可取:-1,-1 - 2kk, -1 + 2kk,-1 + 2kk+1,出现的次数分别为:(22k-1)-2k-1)+2,(2k+1(2k-2)/3,2k-2,(2k+1)(2k-1-1)/3.当l = 1或者2时,满足上述条件相关函数的值同样为:-1,-1 - 2k, -1 + 2k,-1 + 2k+1,出现的次数分别为:(22k-1)-2k-1-1,(2k+1)(2k-2)/3,2k+1,(2k+1)(2k-1+1)/3.
[Abstract]:Low correlation sequences are a kind of special sequences with good algebraic properties. They are widely used in many fields such as radar / CDMA communication systems. Low-correlation sequence functions with the same period have been studied for more than 40 years, especially in recent years, the correlation distribution of m sequences has received extensive attention and many good results. Since the 1970s, Trachtenberg, Niho and Helleseth have written influential papers on the subject. Low correlation sequence distribution with different periods is also an important aspect of correlation sequence distribution. In this paper, let k be an odd number Q = 22k. we study the binary m sequence u (t) and the binary m sequence vl (t) = u (dt l), 0 鈮，

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