Generalized GMW Quadriphase Sequences Satisfying the Welch Bound with Equality

This paper gives new families of quadriphase sequences obtained from large linear complexity sequences over Z ₄ by making use of generalized permutation monomials over Galois rings. The construction of these sequences can be seen as a generalization of the binary GMW sequence construction and hence they are referred to as GGMW sequences over Z ₄. The GGMW families satisfy the Welch bound on inner products with equality and it is shown that the root mean square of all the crosscorrelations and out-of-phase autocorrelations (θ_rms), is approximately equal to the quantity ; L being the period of the sequences. However, θ_max, the maximum magnitude of periodic crosscorrelation and out-of-phase autocorrelation, deviates from the optimal value of . Computer results suggest that the number of crosscorrelation values which deviate from the optimal value of is small. The weight structure of these sequences is the same as those of m-sequences over Z ₄. The linear complexity (LC) of the sequences is computed using a generalized Blahuts theorem on the LC of sequences over Z ₄. Received: January 18, 1999; revised version: October 20, 1999     

两两NQD列的强收敛性质

本文讨论两两NQD随机变量列极限理论中的强收敛性质。首先建立了两两NQD随机变量列最大部分和的Bernstein型概率指数不等式;并在此基础上,给出了具有不同分布的两两NQD列在较弱矩条件下的Petrov型对数律与Wittmann型重对数律,将文献中相应内容从NA情形推广到两两NQD情形。     

New Design of Quaternary Sequences

 We construct new families of quaternary periodic sequences having good autocorrelation properties that are useful for the synchronisation of messages in multiple access communications systems. The design of these quaternary periodic sequences makes use of a general construction based on the Gray map starting from couples of binary words with particular weight or correlation properties. Received: June 26, 2000; revised version: January 21, 2002     

Bayesian Detection of Changepoints in Finite-State Markov Chains for Multiple Sequences

We consider the analysis of sets of categorical sequences consisting of piecewise homogenous Markov segments. The sequences are assumed to be governed by a common underlying process with segments occurring in the same order for each sequence. Segments are defined by a set of unobserved changepoints where the positions and number of changepoints can vary from sequence to sequence. We propose a Bayesian framework for analyzing such data, placing priors on the locations of the changepoints and on the transition matrices and using Markov chain Monte Carlo (MCMC) techniques to obtain posterior samples given the data. Experimental results using simulated data illustrate how the methodology can be used for inference of posterior distributions for parameters and changepoints, as well as the ability to handle considerable variability in the locations of the changepoints across different sequences. We also investigate the application of the approach to sequential data from an application involving monsoonal rainfall patterns. Supplementary materials for this article are available online.     

An Expansion for the Coordinates of the Trace Function over Galois Rings

 The base-2 expansion of the trace sequence over Galois rings of characteristic 2 ^k and size 2 ^km gives rise to k binary coordinate sequences of increasing linear span. An expression for these sequences in terms of elementary symmetric functions is provided. As a byproduct, bounds on the linear span of the coordinate sequences are easily derived. Received: March 4, 1997; revised version: March 24, 1997     

Code optimization for direct sequence spread spectrum and SAW-matched filter implementation

This paper introduces a new optimization algorithm for the minimization of the time sidelobes of the correlation function of a pseudonoise (PN) sequence by applying dynamic weighting to the sequence. The resulting optimized time sidelobe level sequences are to be used in direct sequence spread spectrum (DS-SS) systems with digital modulations such as BPSK, DPSK, QPSK, etc. The new optimization algorithm starts with a PN sequence. It first optimizes the correlation time sidelobes for the case where the consecutive data bits are identical (11 or 00). It then optimizes the correlation time sidelobes for the case of alternating consecutive data bits (10 or 01). The suppressed time sidelobe level sequences are derived by iterating these algorithms alternately starting from the initial PN sequence. The derived suppressed time sidelobe sequences show excellent correlation characteristics when compared to conventional PN sequences such as maximal length sequences, Gold sequences and Barker codes. Surface acoustic wave (SAW) devices were used to implement the optimized time sidelobe level sequences in a matched filter pair. The design of the apodized SAW-matched filters and their predicted second order effects are presented. The experimental results for the SAW-matched filters for the optimized time sidelobe level sequences derived from a Barker code were found to be in good agreement with the theoretical predictions from this new algorithm.     

Zpq上阶数为4的广义割圆序列及其自相关值

本文构造了两类Zpq上阶数为4的广义割圆序列并研究了它们的周期自相关函数,研究结果表明第一类序列具有7值自相关函数,并且当(p-1)(q-1)/16为偶数时,适当选取p,q可以使自相关函数降为6值或5值;当(p-1)(q-1)/16为奇数时,适当选取p,q可以使自相关函数降为5值.第二类序列具有5值自相关函数,并且当口q-p=4时,该序列为3值自相关序列.     

Hexagonal binary arrays with perfect correlation

Two-dimensional binary signals (arrays) with good autocorrelation properties are needed for coded-aperture imaging systems. In many astrophysical instruments, circular detectors with hexagonally packed detector elements are used, such that hexagonal coded apertures are often preferable to rectangular ones. A general method for folding a one-dimensional sequence into a hexagonal array is presented, by which the periodic or odd-periodic correlation properties of the original sequence are preserved. This method is applied to a known family of sequences with perfect odd-periodic correlation, yielding a new family of almost-binary and odd-perfect-or binary and almost odd-perfect-hexagonal arrays with optimum properties for coded-aperture imaging. The new odd-perfect arrays have near-uniform side lengths and exist for many more sizes than known families of even-periodic hexagonal arrays with good imaging properties.     

Kasami序列的多项相关性和正则三项式

通过提出序列多项相关性的概念,本文对Kasami序列进行多项相关分析,得到了Kasami序列的非平凡多项相关值均是三值的,并利用其多项相关性证明了Kasami序列的所有三项式对都是正则三项式对,且具有局部移加特性,据此对Kasami序列进行了移加等价分类,证明了每一类添加全零序列后都构成向量空间,给出了在Kasami序列族中优选近似正交序列的一般方法。     

Periodic Sequences with Maximal Linear Complexity and Large <Emphasis Type="Italic">k</Emphasis>-Error Linear Complexity

The linear complexity and the k-error linear complexity are important concepts for the theory of stream ciphers in cryptology. Keystreams that are suitable for stream ciphers must have large values of these complexity measures. We study periodic sequences over an arbitrary finite field _q and establish conditions under which there are many periodic sequences over _q with period N, maximal linear complexity N, and k-error linear complexity close to N. The existence of many such sequences thwarts attacks against the keystreams by exhaustive search.     

周期二元序列的线性复杂度及其稳定性分析

密码学意义上强的序列不仅应该具有高的线性复杂度而且其线性复杂度必须稳定,k-错线性复杂度用来反应线性复杂度的稳定性。本文基于x~(p~(m_2~n))-1在GF(2)上具有明确的分解式,研究了p~(m_2~n)-周期二元序列的线性复杂度和k-错线性复杂度之间的关系,然后说明了同时使得线性复杂度和k-错线性复杂度都达到最大值的p~(m_2~n)-周期二元序列是存在的。这里p是一个奇素数,2是模p~2的本原根。     

Nonlinear <Emphasis Type="Italic">p</Emphasis>-ary Sequences

Low correlation p-ary sequences with p an odd prime are constructed. They are obtained as Gray images of codewords of a subcode of the generalized Kerdock codes over the ring _p². They can be shown to be nonlinear in some precise sense. The research of this author is partially supported by NUS-ARF research grant R-146-000-029-112 and DSTA research grant R-394-000-011-422.This research was done while this author was visiting Temasek Laboratories and Department of Mathematics, NUS. The author thanks them for their hospitality.Keywords:Galois rings, Gray map, Kerdock code, CDMA.     

两两NQD列的极限定理

本文主要研究了两两NQD列的完全收敛性和强大数定律.文中给出了两两NQD列的定义和推广的Kolmogorov型不等式,并利用推广的Kolmogorov型不等式,得到了两两NQD列的完全收敛性定理.本文构造了两个不增函数,利用不增函数的性质,得到了两两NQD列的强大数定律.本文得到的强大数定律与独立随机变量情况下的强大数定律相类似,进而推广了前人的研究成果.     

Analysis of (k 0 ,k 1 ) clock-controlled sequences

Cryptographic sequence generators are discussed in which a linear feedback shift register (LFSR) is clock controlled in a pseudorandom manner by another register. A model of clock-controlled sequences is proposed. The necessary and sufficient condition guaranteeing the maximal linear complexity and the maximal period of such sequences is given. Two kinds of improved models having better statistical properties are given. In order to study the security of this model, three types of algebraic attacking algorithms are proposed. If the length of the second LFSR in such a model is large, the model can resist our algebraic attacks.     

Spin-rotation invariance and the structure of correlation functions in magnetic systems

We analyze, in the framework of the functional approach to statistical mechanics, general properties of correlation functions in ordered magnetic systems. The aim of this paper is to investigate what consequences can be derived from the requirement of invariance of the theory under local infinitesimal spin rotation. The extension of the method that we introduce, to include anisotropic Hamiltonians, is discussed, and the case of the anisotropy described by an internal field is worked out. Our main results are a set of generalized Ward identities, a microscopic definition of the stiffness constant as a static limit of a local response function, and an exact asymptotic expression for the correlation functions of interest, for zero temperature and small wave length and frequency. Modifications to the hydrodynamic expression for correlation functions in the case where anisotropy is present are also discussed.     

On quasi-cyclic codes over {\mathbb{Z}_q}

Quasi-cyclic (QC) codes are a remarkable generalization of cyclic codes. Many QC codes have been shown to be best for their parameters. In this paper, some structural properties of QC codes over the prime power integer residue ring ${\mathbb{Z}_q}$ are considered. An l-QC code of length lm over ${\mathbb{Z}_q}$ is viewed both as in the conventional row circulant form and also as a ${\frac{\mathbb{Z}_q[x]}{\langle x^m-1 \rangle}}$ -submodule of ${\frac{GR(q,l)[x]}{\langle x^m-1 \rangle}}$ , where GR(q, l) is the Galois extension ring of degree l over ${\mathbb{Z}_q}$ . A necessary and sufficient condition for cyclic codes over Galois rings to be free is obtained and a BCH type bound for them is also given. A sufficient condition for 1-generator QC codes to be ${\mathbb{Z}_q}$ -free is given and a formula to evaluate their ranks is derived. Some distance bounds for 1-generator QC codes are also discussed. The duals of QC codes over ${\mathbb{Z}_q}$ are also briefly discussed.     

铺层方式对CFRP-Al单搭接接头胶接性能的影响

使用热压罐制备[45/-45]_4s、[0/90]_4s和[0/45/-45/90]_2s三种铺层方式的CFRP层合板,然后在室温下与Al胶接制备出单搭接试样。使用电子万能试验机、数字图像相关法(DIC)和扫描电子显微镜(SEM)等手段测量胶接接头的拉伸载荷-位移曲线和应变分布并观察断口形貌。基于试验数据分析不同铺层方式下CFRP-Al单搭接接头的拉伸性能,研究了铺层方式对CFRP-Al单搭接接头胶接性能的影响和铺层方式胶接接头的破坏机制。结果表明,在拉伸过程中[45/-45]_4s试样出现塑性变形阶段其拉伸位移最大,而[0/45/-45/90]_2s和[0/90]_4s试样的拉伸位移较小且发生了脆性断裂。铺层方式从[45/-45]_4s到[0/45/-45/90]_2s再到[0/90]_4s,试样的极限载荷和纤维束断裂数量增加、层间剪切力减小、应变集中程度和分层破坏程度降低。     

Features of heat transfer for current-stabilized conductors

Fluctuation regimes of heat transfer of current-stabilized conductors have been discovered and investigated, characterized by the fact that the stochastic time variation of both local temperatures and temperatures that are integral over the length of the conductor vary in time, attaining recurring minimal and maximal values. A physical model of the fluctuation mechanism of heat transfer is proposed, and correlation relationships are given to calculate fluctuation regimes.Translated from Inzhenerno-fizicheskii Zhurnal, Vol. 61, No. 5, pp. 795–803, November, 1991.     

Some Power Mappings with Low Differential Uniformity

 Differentially uniform power mappings of the form f (x)=x ^d over GF(p ⁿ ) are considered. We construct an infinite family of 2-uniform mappings in the binary case. In the nonbinary case we give two large families of k-uniform mappings with low values of k. We also show how to construct families of sequences from differentially 1-uniform power mappings, which have parameters as good as the best presently known comparable families of sequences. Received: November 4, 1996; revised version: February 14, 1997     

Planar four node piezoelectric elements with drilling degrees of freedom

Several new planar four node piezoelectric elements with drilling degrees of freedom are presented. We begin by deriving two families of variational formulations accounting for piezoelectricity and in‐plane rotations. The first family retains the skew‐symmetric part of the stress tensor, while in the second, the skew part of stress is eliminated from the functional. The finite elements derived from two of the variational formulations derived in this paper are investigated. The first element is based on an ‘irreducible’ form, while the other is based on a fully mixed functional, with both stress and electric flux density assumed. Our new elements are shown to be accurate and robust in comparison with a number of existing elements, for several benchmark test problems. Copyright © 2005 John Wiley & Sons, Ltd.