【摘要】：低相關序列是一類有著很好代數(shù)性質的特殊序列,它被廣泛應用于雷達,CDMA通信系統(tǒng)等多個領域.具有相同周期的低相關序列函數(shù)已經研究了將近40多年,特別是近些年來m序列的相關分布受到了廣泛的關注和研究也有很多很好的成果.從20世紀70年代以來,Trachtenberg, Niho和Helleseth寫了很多關于這個方面有影響力的論文.不同周期的低相關序列分布也是相關序列分布的一個重要方面.本文令k為奇數(shù),q = 22k,研究了周期為q - 1的二元m序列u(t)和周期為(q - 1)/3的二元m序列vl(t) = u(dt + l), 0 ≤ l ≤ 2,其中d和s分別滿足d = (2kk - 1)s + 1和(22r+ ) ≡1(mod2k + 1)的相關分布情況.我們運用了有限域上二次型理論以及一些代數(shù)方程組求解技巧等確定了滿足上述條件的相關分布是一個四值分布.當l = 0時,我們得出滿足上述條件相關函數(shù)的值可取:-1,-1 - 2kk, -1 + 2kk,-1 + 2kk+1,出現(xiàn)的次數(shù)分別為:(22k-1)-2k-1)+2,(2k+1(2k-2)/3,2k-2,(2k+1)(2k-1-1)/3.當l = 1或者2時,滿足上述條件相關函數(shù)的值同樣為:-1,-1 - 2k, -1 + 2k,-1 + 2k+1,出現(xiàn)的次數(shù)分別為:(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，

本文編號：2257721