环Zpl导出Kerdock-code序列的部分周期性质

对环Z_p^l导出的多元Kerdock-code序列的部分周期性质进行了研究,这里p为任意奇素数,l为任意正整数.利用特征为p^l的Galois环上不完全指数和的非平凡上界,对上述p元Kerdock-code序列的非周期自相关性及互相关性进行了估计,同时对序列的部分周期分布和部分周期独立r-样式分布也进行了刻画.结果表明,此类序列具有极低的非周期自相关性及互相关性,同时其部分周期分布和部分周期独立r-样式分布也是渐进均匀的,在密码学和通信领域具有潜在的应用价值.     

Z4上周期为2p2的四元广义分圆序列的线性复杂度

该文根据特征为4的Galois环理论,在Z₄上利用广义分圆构造出一类新的周期为2p2(p为奇素数)的四元序列,并且给出了它的线性复杂度。结果表明,该序列具有良好的线性复杂度性质,能够抗击Berlekamp-Massey (B-M)算法的攻击,是密码学意义上性质良好的伪随机序列。     

Galois环上的一类GMW序列及其线性复杂度

将有限域上GMW序列的概念推广到了一般的Galois环上.利用环上的置换,定义了一类新的一般Galois环上的GMW序列,并对其线性复杂度进行了估计.结果表明,这类GMW序列具有非常大的线性复杂度.     

环Z/(p~d)上多项式周期的特性

设f(x)是环Z/(p~d)上首一多项式,则f(x)可自然视为Z/(p)上多项式,其中i=1,2,…,d。本文刻划了在各层环Z/(p),2/(p~2),…,Z/(p~d)上f(x)的周期变化情况。     

置换多项式在密码中的应用

1 置换多项式与密码体系设f(x)是一个整系数多项式,m>1是整数,当x过模m的一个完全剩余系,f(x)也过模m的一个完全剩余系,则称f(x)是模m的一个置换多项式。此时,f(x)正好导出{0,1,…,m-1}的一个置换,f(x)也叫模m剩余类环Z/(m)上的一个置换多项式。当m=p是一个素数时,则称f(x)是有限域F_p上的一个置换多项式。如果q=p~1,类似地可定义有限域F_q上的置换多项式。     

环F2+uF2的Galois扩张上的迹码

环E＋uF2是介于环Z4与域F4之间的一种四元素环，因此分享了环Z4与域F4的一些好的性质，此环上的编码理论研究成为一个新的热点。该文给出了环E＋uF2的Galois扩张的相关理论，指出此Galois扩环的自同构群不同于Z4环上的Galois扩环的自同构群；定义了Galois扩环上的迹码的概念及子环子码的概念，证明了此Galois扩环上的一个码的对偶码的迹码是该环的子环子码的对偶码。     

重模剩余类环的一一幂变换及其在保密通信中的应用

本文讨论在一类重模剩余类环上建立公钥密码体制的条件,主要结果是:设域F=GF(p),p为素数,f_1(x),f_2(x),…,f_3(x)是多项式环F[x]上两两互素的不可约多项式,deg f_i(x)=n_i,i=1,2,…,s。sum from i=1 to s(n_i)=n, 设f(x)=multiply from i=1 to s(f_i(x)),则deg f(x)=n。定义重模剩余类环F[x]/(f(x))的幂变换为σ_k:α→α~k(moddp,f(x)),α∈F[x]/(f(x)),k∈N,当且仅当k∈Z_q~*时,σ_k为F[x]/(f(x))的一一幂变换,这里q=[p~(n1)-1,p~(n2)-1,…,p~(ns)-1],Z_q~*表示整数模q的缩系。     

剩余类环上序列采样簇的结构

本文研究了采样簇G~(S)(f(x))的结构,并给出了采样序列的特征多项式。     

环F2+uF2的Galois扩张上的迹码

环F2+uF2是介于环Z4与域F4之间的一种四元素环,因此分享了环Z4与域F4 的一些好的性质,此环上的编码理论研究成为一个新的热点。该文给出了环F2+uF2 的Galois扩张的相关理论,指出此Galois扩环的自同构群不同于Z4环上的Galois扩环的自同构群;定义了Galois扩环上的迹码的概念及子环子码的概念,证明了此Galois扩环上的一个码的对偶码的迹码是该环的子环子码的对偶码。     

环Fq+uFq+...+uh-1Fq上任意长度的(u?-1)-常循环码

该文利用环同态理论,给出了环k 1 q q q R F uF u F =++L+-上任意长度N 的所有(ul -1)-常循环码的生成元, l 是R 的可逆元.证明了[]/1 N R x < x +-ul >是主理想环.给出了环R上任意长度N 的(ul -1)-常循环码的计数.确定了环R上任意长度N 的(ul -1)-常循环码的最高阶挠码的生成多项式,由此给出了环R上长度 s p 的所有(ul -1)-常循环码的汉明距离.     

Pseudonoise sequences based on algebraic feedback shift registers

Over the past half century, various statistical properties of pseudorandom sequences have played important roles in a variety of applications. Among these properties are Golomb's randomness conditions: (R1) balance, (R2) run property, and (R3) ideal autocorrelations, as well as the closely related properties (R4) shift and add, and (R5) de Bruin (uniform distribution of subblocks). The purpose of this paper is to describe the relationships among these conditions, and to introduce a new method for generating sequences with all these properties, using algebraic feedback shift registers.     

Compression mappings on primitive sequences over Z/(p/sup e/)

Let Z/(p/sup e/) be the integer residue ring with odd prime p/spl ges/5 and integer e/spl ges/2. For a sequence a_ over Z/(p/sup e/), there is a unique p-adic expansion a_=a_/sub 0/+a_/spl middot/p+...+a_/sub e-1//spl middot/p/sup e-1/, where each a_/sub i/ is a sequence over {0,1,...,p-1}, and can be regarded as a sequence over the finite field GF(p) naturally. Let f(x) be a primitive polynomial over Z/(p/sup e/), and G'(f(x),p/sup e/) the set of all primitive sequences generated by f(x) over Z/(p/sup e/). Set /spl phi//sub e-1/ (x/sub 0/,...,x/sub e-1/) = x/sub e-1//sup k/ + /spl eta//sub e-2,1/(x/sub 0/, x/sub 1/,...,x/sub e-2/) /spl psi//sub e-1/(x/sub 0/,...,x/sub e-1/) = x/sub e-1//sup k/ + /spl eta//sub e-2,2/(x/sub 0/,x/sub 1/,...,x/sub e-2/) where /spl eta//sub e-2,1/ and /spl eta//sub e-2,2/ are arbitrary functions of e-1 variables over GF(p) and 2/spl les/k/spl les/p-1. Then the compression mapping /spl phi//sub e-1/:{G'(f(x),p/sup e/) /spl rarr/ GF(p)/sup /spl infin// a_ /spl rarr/ /spl phi//sub e-1/(a_/sub 0/,...,a_/sub e-1/) is injective, that is, a_ = b_ if and only if /spl phi//sub e-1/(a_/sub 0/,...,a_/sub e-1/) = /spl phi//sub e-1/(b_/sub 0/,...,b_/sub e-1/) for a_,b_ /spl isin/ G'(f(x),p/sup e/). Furthermore, if f(x) is a strongly primitive polynomial over Z/(p/sup e/), then /spl phi//sub e-1/(a_/sub 0/,...,a_/sub e-1/) = /spl psi//sub e-1/(b_/sub 0/,...,b_/sub e-1/) if and only if a_ = b_ and /spl phi//sub e-1/(x/sub 0/,...,x/sub e-1/) = /spl psi//sub e-1/(x/sub 0/,...,x/sub e-1/) for a_,b_ /spl isin/ G'(f(x),p/sup e/).     

Segmented loop antenna for UHF near-field RFID applications

A segmented loop antenna is presented for ultra-high frequency (UHF) near-field radio frequency identification (RFID) applications. The proposed segmented configuration makes the current along the loop remain in-phase even though the perimeter of the loop is comparable to the operating wavelength, so that a strong and uniform magnetic field is generated in the region surrounding the antenna. The antenna printed on a FR4 printed circuit board (PCB) with an overall size of 160 x 180 x 0.5 mm achieves good impedance matching and uniform magnetic field distribution over an operating bandwidth of 800?1040 MHz, which is desirable for UHF near-field RFID reader applications.     

Orthogonal multilevel pseudorandom sequences and impulse sequences derived from them

Constructions are given of sets of orthogonal multilevel pseudorandom sequences with binomial and uniform amplitude distributions. The sequences are based on binary maximal-length sequences and have similar correlation properties to those sequences. Pseudorandom impulse sequences suitable for nerve impulse simulation are constructed from the uniform-amplitude distribution sequences, and empirical bounds are established on their correlation performance.     

Fast algorithms for measurement-based traffic modeling

This paper develops fast algorithms for the construction of a circulant modulated rate process to match with the two primary traffic statistical functions: rate distribution f(x) and autocorrelation R(τ). Using existing modeling techniques, f(x) has to be limited to certain forms such as Gaussian or binomial; R(τ) can only consist of one or two exponential terms which are often real exponentials rather than complex. In reality, these two functions are collected from real traffic traces and generally expressed in a very complicated form. We only consider the traffic whose correlation function can be approximated by the sum of complex exponentials. Our emphasis is placed on the algorithm design for matching complicated R(τ) in traffic modeling. The typical CPU time for traffic modeling with R(τ) consisting of five or six complex exponential terms is found to be in the range of a few minutes by the proposed algorithms. Our study further shows an excellent agreement between the original traffic traces and the sequences generated by the matched analytical model. The selection of the measurement-window in traffic statistics collection for queueing performance analysis is also discussed     

Irreducible Polynomials Which Divide Trinomials Over GF (2)

The simplest linear shift registers to generate binary sequences involve only two taps, which corresponds to a trinomial over GF(2). It is therefore of interest to know which irreducible polynomials f(x) divide trinomials over GF(2), since the output sequences corresponding to f(x) can be obtained from a two-tap linear feedback shift register (with a suitable initial state) if and only if f(x) divides some trinomial t(x)=x^m+x^a+1 over GF(2). In this paper, we develop the theory of which irreducible polynomials do, or do not, divide trinomials over GF(2). Then some related problems such as Artin's conjecture about primitive roots, and the conjectures of Blake, Gao, and Lambert, as well as of Tromp, Zhang, and Zhao are discussed     

Chaotic frequency hopping sequences

This letter describes a novel family of frequency hopping sequences generated by chaotic systems. The sequences give a uniform spread over the entire frequency bandwidth. In addition to having good Hamming correlation properties, they possess ideal linear span. The sequences produce almost as good performance as random hopping patterns when used in frequency hopping code-division multiple-access (FH/CDMA) systems. Many numerical examples based on a digital chaos generator are presented     

On ternary complementary sequences

A pair of real-valued sequences A=(a₁,a₂,...,a_N) and B=(b₁,b ₂,...,b_N) is called complementary if the sum R(·) of their autocorrelation functions R_A(·) and R_B(·) satisfies R(τ)=R_A(τ)+R _B(τ)=Σ_i=1^N$ -^τa_ia_i+τ+Σ_j=1 ^N-τb_jb_j+τ=0, ∀τ≠0. In this paper we introduce a new family of complementary pairs of sequences over the alphabet α₃=+{1,-1,0}. The inclusion of zero in the alphabet, which may correspond to a pause in transmission, leads both to a better understanding of the conventional binary case, where the alphabet is α₂={+1,-1}, and to new nontrivial constructions over the ternary alphabet α₃. For every length N, we derive restrictions on the location of the zero elements and on the form of the member sequences of the pair. We also derive a bound on the minimum number of zeros necessary for the existence of a complementary pair of length N over α₃. The bound is tight, as it is met by some of the proposed constructions, for infinitely many lengths     

Huffman sequences with approximately uniform envelopes or cross-correlation functions (Corresp.)

The question of whether uniform Huffman (impulse equivalent) sequences exist is discussed, and some necessary conditions for a Huffman sequence to be uniform are mentioned. A comprehensive search revealed that no uniform Huffman sequences exist from lengths 4 to 17, inclusive. A procedure is described for synthesizing pairs of Huffman sequences whose cross-correlations are approximately uniform and, incidentally, are also themselves Huffman sequences.     

CONSTRUCTING AND ANALYZING A CLASS OF CONTROLLABLE SEQUENCES

By using m-sequence over the finite field GF(2m) of degree L to control m-sequence over GF(2m) of degree L, a class of periodic sequences with large linear complexity is constructed. The lower bounds of the linear complexity of these sequences are L((L +1)m-Lm).