扩展Kasami序列的相关特性

利用有限域上二次型理论讨论了ｐ（ｐ为奇素数）元Ｋａｓａｍｉ序列一种扩展形式的相关特性，求出了扩展Ｋａｓａｍｉ序列的相关函数值，证明在一定条件下，扩展Ｋａｓａｍｉ序列最大自相关旁瓣值和最大互相关模值可以接近Ｗｅｌｃｈ下限．     

一类最优跳频序列族的代数构造

在通信系统中,直接序列扩频和跳频扩频是两种最主要的扩散编码技术.而在FHCDMA系统中,跳频序列被广泛使用.利用分圆法和离散对数函数,首先构造了一类具有新参数的跳频序列族,并给出了各类汉明相关值的计算公式.其次,证明了所构造的跳频序列(族)所具有的最优性.     

基于广义分圆法的一类跳频序列族

平均汉明相关值是评价跳频序列族性能的一个重要参数.本文在Whiteman广义分圆法的基础上构造了一类新的跳频序列族,随后证明了其关于平均汉明相关界是最优的,并给出了各类汉明相关值的计算公式.     

基于广义分圆法的一类素数幂周期跳频序列

关于素数幂p~m(m1),首先给出了一类新的广义分圆及其性质;其次,基于此广义分圆法构造了一类周期为p~m的跳频序列族;最后证明了该序列族关于平均汉明相关界是最优的,而且当m=2时该序列族关于最大汉明相关界也是最优的.     

NA序列广义Jamison型加权和的几乎处处收敛性

本文从随机变量序列广义Ｊａｍｉｓｏｎ型加权和的一个系数指标函数自身性质出发，讨论了广义Ｊａｍｉｓｏｎ型加权和的强稳定性，避免了控制函数的引入， 进一步还得到了更一般的ＮＡ序列广义Ｊａｍｉｓｏｎ型加权和的几乎处处收敛的条件，并将前人的若干结论包含为特例．     

贪婪t－相交有限序列族

设Ｆ为有限序列族，对ａ＝（ａ１，ａ２，…，ａｎ）∈Ｆ，ａｉ为整数且０≤ａｉ≤ｓｉ（整数），记ｓ（ａ）＝｛ｊ｜１≤ｊ≤ｎ，ａｊ＞０｝，ｓ（Ｆ）＝｛ｓ（ａ）｜ａ∈Ｆ｝，及Ａ｛１，２，…，ｎ｝时Ｗ（Ａ）＝Пｉ∈Ａｓｉ．称Ｆ为贪婪ｔ－相交，如对任何ａ，ｂ∈Ｆ，至少有ｔ个ａｉ，ｂｉ＞０，且Ｗ（Ａ）≥Ｗ（（｛１，２，…，ｎ｝－Ａ）＋Ｂ）对任何Ａ∈Ｓ（Ｆ）及ＢＡ（｜Ｂ｜＝ｔ－１）成立．本文得到当ｓ１＞ｓ２＞…＞ｓｎ时的最大贪婪ｔ－相交有限序列族．     

广义Lucas序列的重复度与相关的不定方程的解数

用ｐ－ａｄｉｃ分析方法讨论了广义Ｌｕｃａｓ序列的重复度,并由此证明了不定方程ａｘ＾２＋Ｄ＝ｃｐ＾ｎ,ｘ〉０,ａＤ〉０,ｃ＝１,２,４,ｐ为素数,除四种例外情形外,最多只有两组解（ｘ,ｎ）。     

次最优跳频序列集的构造

分圆类和分圆数是数论和组合数学中的经典议题.它们与差集,序列设计,以及编码理论存在着密切的关联.而寻求和设计比较理想(最优及次最优)的跳频序列(集)则是研究跳频通信技术的重要课题.文章基于广义分圆类提出一种次最优跳频序列集的构造,这些序列集具有新的参数且序列长度能为任意大于3的奇数.     

Wiener空间上最佳一致逼近的平均误差的渐近估计

设Ｔｍ是ｍ阶积分算子，Ｋｍ是ｍ阶线性常微分算子Ｌｍ的逆算子．关于Ｗｉｅｎｅｒ测度，本文得到Ｔｍ与Ｋｍ的多项式最佳一致逼近的平均误差及ｎ－最优平均信息半径的最优阶．主要结果是Ｅａｎ（Ｔｍ，Ｗ）ｐ，∞ｎ－ｍ－１２（ｌｎｎ）１２及ｒｓｔｎ（Ｔｍ，Ｗ）ｐ，∞ｒｓｔ（Ｋｍ，Ｗ）ｐ，∞ｎ－ｍ－１２（ｌｎｎ）１２．     

几何序列与拟广义几何序列的互相关函数

本文构造了一类与几何序列的互相关特性非常好的新序列－拟广义几何序列。     

A new frequency-hopping sequence set based upon generalized cyclotomy

In this paper, a new set of frequency-hopping sequences is proposed, and the Hamming correlation distribution of the new set is investigated. The construction of new frequency hopping sequences is based upon generalized cyclotomy. It is shown that the proposed frequency-hopping sequence set is optimal with respect to the average Hamming correlation bound.     

Constructions of optimal low-hit-zone frequency hopping sequence sets

In recent years, the study relating to low-hit-zone frequency hopping sequence sets, including the bounds on the Hamming correlations within the low hit zone and the optimal constructions, has become a new research area attracting the attention of many related researchers. In this paper, two constructions of optimal frequency hopping sequence sets with low hit zone have been employed, one of which is based on m-sequence while the other is based on the decimated sequences of m-sequence. Moreover, in the special case of \(k=n-1\), the construction based on the decimated sequences of m-sequence also yields low-hit-zone frequency hopping sequence sets with optimal periodic partial Hamming correlation property.     

Construction of low-hit-zone frequency hopping sequences with optimal partial Hamming correlation by interleaving techniques

In quasi-synchronous frequency hopping code division multiple-access systems, frequency hopping sequences (FHSs) with low-hit-zone (LHZ) are commonly employed to minimize multiple-access interferences. Usually, the length of correlation window is shorter than the period of the chosen FHSs due to the limited synchronization time or hardware complexity. Thus the study of the partial Hamming correlation properties of LHZ FHSs is of particular importance. In this paper, we prove the nonexistence of LHZ FHS sets with strictly optimal partial Hamming correlation in some conditions. In addition, employing the interleaving techniques, we present a construction of LHZ FHS sets with optimal partial Hamming correlation from m-sequences. The fundamental idea of our design is to use short individual m-sequences together with certain appropriate shift sequences to construct long LHZ FHS sets with optimal partial Hamming correlation. In particular, our construction gives new parameters not covered in the literature.     

New designs of frequency hopping sequences with low hit zone

Frequency hopping sequences have been found wide applications in various modern frequency hopping spread spectrum communications and radar systems. With potential applications to these areas such as ultra wide bandwidth time hopping code division multiple access radio systems, multi-user and sonar systems, the design of quasi-synchronous time/frequency hopping code division multiple access systems by employing low hit zone hopping sequences has attracted wide attentions. In this paper, we present three construction methods for the low Hamming correlation zone frequency hopping sequences. The parameters of these sets of frequency hopping sequences with low hit zone are new and flexible. The constructed sequences are almost optimal and optimal respectively with respect to the Peng?CFan?CLee bounds. The simplicity of this technique makes it attractive for practical use.     

Low-hit-zone frequency hopping sequence sets with optimal partial Hamming correlation properties

In order to evaluate the goodness of frequency hopping sequence (FHS) design, the periodic Hamming correlation function is used as an important measure. Usually, the length of correlation window is shorter than the period of the chosen FHS, so the study of the partial Hamming correlation of FHS is particularly important. In this paper, a class of low-hit-zone (LHZ) FHS sets with good partial Hamming correlation properties which has not yet been reported previously is constructed based on interleaving techniques. It is shown that new FHS sets are optimal with respect to the partial Hamming correlation bound of FHSs with LHZ.     

A NEW FAMILY OF BINARY SEQUENCES WITH OPTIMAL AUTOCORRELATION VALUES AND NICE PSEUDO-RANDOM PROPERTIES

In this paper we present a series of binary sequences which is a generalization of GMW sequences constructed by Scholtz and Welch. Our sequences have optimal autocorrelation values as m -sequences, and nice pseudo-random property. The number of such sequences is counted and the linear span of such sequences is evaluated.     

一类新的广义零差分平衡函数及其应用

2008-2009年,丁存生在构造最佳常组合码与优化及完善差分系统中首次引入了零差分平衡(简称ZDB)函数的概念,据此学者们构造出了最佳组成权重码和最优跳频序列.作者将零差分平衡函数的定义推广到一般的广义零差分平衡函数,并利用2分圆陪集构造了一类广义零差分平衡函数,由此构造出一类新的常组合码和差分系统.     

一种OLS/OOC二维光正交码的构造与性能分析

利用不同的序列作为波长跳频序列和时间扩频序列可以构造出不同的二维光正交码在众多文献中已有所报道.在经过正交拉丁方(OLS)与跳频序列的相关性研究之后.做了以下主要工作:首先,将正交拉丁方(OLS)序列作为波长跳频序列,结合一维时间扩频序列(OOC),构造了一种OLS/OOC二维光正交码.然后,本文对构造的OLS/OOC进行了多种性能仿真和分析.相对于PC/OOC、OCFHC/OOC等二维光正交码而言,OLS/OOC的波长数并不局限于素数,更能充分利用MWOCDMA系统中的有效波长数.仿真和分析表明:码字具有很好的相关性能,码字容量直逼理论极限,为一种渐近最优二维光正交码.     

GMW序列的迹表示

研究了长度为2n-1的二元GMW序列的迹表示,用从F2n到F2的迹函数的和式给出了GMW序列的一种简洁的迹表示,并且通过这种迹表示得到了一种新的快速生成GMW序列的方法和一种求GMW序列的极小多项式的方法.最后,还证明了两个GMW序列具有相同极小多项式的一个充要条件.