论文标题
二进制$ m $序列的算术自相关分布
Arithmetic autocorrelation distribution of binary $m$-sequences
论文作者
论文摘要
二进制$ m $ - 序列是最大的周期$ n = 2^m-1 $的二进制序列，该二进制序列由线性移位寄存器（长度$ m $）产生。他们在通信中具有广泛的应用，因为它们具有几种理想的伪随身界，例如平衡，统一模式分布和理想的（经典）自相关。 Mandelbaum \ cite {9mand}在对算术代码的研究中，引入了2次版本的二进制序列的经典自相关，称为算术自相关。后来，Goresky和Klapper \ cite {3G1,4G2,5G3,6G4}将此概念推广到非二进制案例，并开发了与带有随身携带的线性移位寄存器相关的算术自相关的几种属性。最近，Z. Chen等。 \ cite {1c1}显示了二进制$ m $序列算术自相关的上限，并提出了对算术$ m $序列算术自相关的绝对价值分布的猜想。
Binary $m$-sequences are ones with the largest period $n=2^m-1$ among the binary sequences produced by linear shift registers with length $m$. They have a wide range of applications in communication since they have several desirable pseudorandomness such as balance, uniform pattern distribution and ideal (classical) autocorrelation. In his reseach on arithmetic codes, Mandelbaum \cite{9Mand} introduces a 2-adic version of classical autocorrelation of binary sequences, called arithmetic autocorrelation. Later, Goresky and Klapper \cite{3G1,4G2,5G3,6G4} generalize this notion to nonbinary case and develop several properties of arithmetic autocorrelation related to linear shift registers with carry. Recently, Z. Chen et al. \cite{1C1} show an upper bound on arithmetic autocorrelation of binary $m$-sequences and raise a conjecture on absolute value distribution on arithmetic autocorrelation of binary $m$-sequences.
