非线性等距码和等距等重码的上界

设Qq(n,d)代表码长为n、任意两个不同码字间的Hamming距离为d的q元等距码所能达到的最大可能码字数(不考虑码的重量);Eq(n,d,w)代表码长为n、任意两个不同码字间Ham-ming距离为d、每个码字重量为w的q元等距等重码所能达到的最大可能码字数量.设q,n,d,w∈N,获得当q＞2时,有①Eq(n,d,w)≤qn,②Qq(n,d)≤qn+1;当q=2时,则有③Eq(n,d,w)≤n,④Qq(n,d)≤n+1.     

有限域上m序列与其采样序列的互相关性

本文研究了有限域GF(p)上的m序列与其采样序列之间的互相关函数C_d(t),得到以下结论:(1)当采样因子d= pⁿ+1 p+1 + pⁿ-1 2 ,n为奇数且p≡3(mod 4)时,|1+C_d(t)| 1+p 2 pⁿ ,从而解决了Muller在文献 中提出的一个公开问题,并将文献[1]中的p=3时的结论推广为一般情形;(2)当d= pⁿ+1 p+1 ,n为奇数且p≡3(mod 4)时,C_d(t)∈{-1,-1+ p n+1 -1- pⁿ⁺¹ };(3)在以上两种情况下,对|1+C_d(t)|关于t的分布进行了研究,结果表明,当p很大时,|1+C_d(t)|取最大值的概率很小.     

新的具有大线性复杂度的4值低相关序列集

设正整数n、m和r满足n=4m,r=2m-1 -1,基于Niho序列集和d型函数构造了一类4值低相关序列集S(r).该序列集中序列的数目为2n,相关函数的最大边峰值2(n+2)/2+1,序列的周期为2n-1.通过Key的方法,证明了该序列集中序列线性复杂度的F界为n(2n/2-3+2).该序列集与江文峰等人构造的序列集具有相同的相关函数值和序列数目,但拥有更大的线性复杂度.     

无铅压电材料NBT-BZT陶瓷压电性能及改性

通过配方试验和性能测试分析研究了(1x)Na1/2Bi1/2TiO3-xBa[ZryTi(1y)]O3(x=0.04,0.06,0.08,0.10,y=0.04,0.045,0.05,0.06)无铅压电陶瓷的压电、介电性能。以及当x=0.06,y=0.045时引入Sn4+对NBT-BZT材料的压电介电性能影响。研究表明:当x=0.06,y=0.045, Sn4+对(Na1/2Bi1/2)2+取代量为0.02时,系统的压电性能参数d33和kt分别达到196 pC/N和0.55,相对介电常数可提高到1 263。     

线性移位寄存器在安全RSA模数中应用的研究

运用线性移位寄存器(LFSR)序列模2个不同素数时的周期一般不同这一性质,尝试构造分解另一类RSA模数的方法;指出对于RSA模数n=pq的一个素因子P,当P2+p+1,P3+P2+p+1,…其中之一仅含有小的素因子时,给出的算法能够分解合数n=pq,并给出了一个基于三级LFSR分解合数的实例来说明算法的具体运算步骤.根据该分解算法,在选取RSA模数时,为确保安全性,除避免已知的不安全因素以外,还需要保证n的素因子P满足P2+P+1,P3+P2+P+1,…均包含大的素因子.     

高陡度系数有源带通滤波器的设计与调试

一、概述由网络理论可知,滤波器的频响特性可用下式传递函数H(s)表示H(s)=V_0(s))/(V_4(s)=a_ms~m+a_(m-1)s~(m-1)+…+a_1s+a_0/b_ns~n+b_(n-1)s~(n-1)+…+b_1s+b_0 式中a、b为实常数;m、n=1,2,…(m≤n);s为复频率(s=jw);V_0(s)代表输出信号,它的每个根值代表一个零点;V_i(s)代表输入信号,每个根对应一个极点。一个n阶传递函数可分解成H_1,H_2,…,H_n各因式的乘积,每一因式可计算得一个滤波节,将各滤波节电路级联后就成为具有n阶传递函数特性的滤波器。现代网络理论已获得一系列各具特色的、标准传递函数。     

新的Ⅱ型偶长Z-互补对构造

为丰富Z-互补对(ZCP)的参数形式,研究了新的Ⅱ型ZCP的构造方法。基于迭代法,实现了Ⅱ型(2^k+2N,(2^k+2-1)N)-ZCP的构造,当N=1时,可得Z-最优Ⅱ型(2^k+2,(2^k+2-1))-ZCP。进一步,将迭代法与插值法相结合,构造了Ⅱ型(2^k+1N+2^k+1,2^k+1N+2^k+1-N/2)-ZCP;当N=2时,可得Z-最优Ⅱ型(3×2^k+1,3×2^k+1-1)-ZCP。所提方法可以生成新的偶长ZCP,实现了对现有ZCP数量的扩展。     

海洋大气湍流对激光通信系统性能的影响分析

大气湍流引起光波强度在光束截面内的闪烁,降低了激光通信系统的信噪比.应用基于Rytov近似的激光大气传输光强起伏理论模型,在局地均匀各向同性Kolmogolov湍流谱的假设条件下,对大气湍流引起的光强起伏进行了分析.并从信号检测理论出发,将大气湍流与激光通信系统误码率指标相结合.分析结果表明,在典型的海洋大气湍流环境下,以误码率指标衡量,随着C2n的增加,激光通信系统的有效作用距离大大缩短,当C2n达到5×10-15m-2/3时,通信的有效距离不足2 km,当C2n达到3×10-14m-2/3时,通信的有效距离降至1 km以下.     

对强化MD结构杂凑函数的一个新的“牧群”攻击

该文构造了具有2k个起始点的变长"钻石树"结构的多碰撞,并据此提出了对强化MD结构杂凑函数的一个新的选择目标强制前缀且原像长度为2k+3块的原像攻击(即"牧群"攻击).由于增大了攻击过程中可利用的中间链接值的数量,故当k≤n/4-1.05时,新的牧群攻击可将该攻击的计算复杂性由现有结果O(2n-2(k+1)+2n/2+k+5+2)降至O(2n-k/3+2n/2+k+2).     

PNiTa-PZT三元系压电陶瓷性能

采用传统陶瓷工艺制备了0.02Pb(Ni1/3Ta2/3)O3+0.98Pb(ZrxTi1–x)O3(x=0.50~0.55,PNiTa-PZT)三元系压电陶瓷,研究了n(Zr)/n(Ti)变化对陶瓷性能的影响。结果表明:随其比值的变化,陶瓷样品均为钙钛矿结构,且对陶瓷显微结构影响不大;当n(Zr)/n(Ti)为52/48时,陶瓷具有较优的压电、介电性能:kp为0.583,d33为266pC/N,tC为394℃,tanδ为0.0055,ε3T3/ε0为1297。其中tC比目前文献报道的PZT基压电材料高30~50℃,有望在高温压电陶瓷领域获得应用。     

New family of single-error correcting codes

A construction is given that combines an(n, M_1, d_1)code with an(n, M_2, d_2 = [frac{1}{2}(d_1 + 1)])code to form a(2n, M_1 M_2, d_1)code. This is used to construct a new family of nongroup single-error correcting codes of all lengthsnfrom2^mto 3 ·2^{m-1} - 1, for everym geq 3. These codes have more codewords than any group code of the same length and minimum distance. A number of other nongroup codes are also obtained. Examples of the new codes are (16,2560,3) and (16,36,7) codes, both having more codewords than any comparable group code.     

Calculation of transient response

Given the rational algebraic function X(s) = an?1Sn?1+an?2Sn?2+?+a1s+a0/sn+bn?1sn?1+?+b1s+b0 it is shown that the corresponding time function is expressed simply by the linear combination x(t) = an?1qn?1(t)+an?2qn?2(t) +? +a1q1(t) + a0q0(t) where functions qt(t) are the last column elements of the transition matrix M(t) = exp (At).     

Weight enumerator for second-order Reed-Muller codes

In this paper, we establish the following result. Theorem:A_i, the number of codewords of weightiin the second-order binary Reed-Muller code of length2^mis given byA_i = 0unlessi = 2^{m-1}or2^{m-1} pm 2^{m-l-j}, for somej, 0 leq j leq [m/2], A_0 = A_{2^m} = 1, and begin{equation} begin{split} A_{2^{m-1} pm 2^{m-1-j}} = 2^{j(j+1)} &{frac{(2^m - 1) (2^{m-1} - 1 )}{4-1} } \ .&{frac{(2^{m-2} - 1)(2^{m-3} -1)}{4^2 - 1} } cdots \ .&{frac{(2^{m-2j+2} -1)(2^{m-2j+1} -1)}{4^j -1} } , \ & 1 leq j leq [m/2] \ end{split} end{equation} begin{equation} A_{2^{m-1}} = 2 { 2^{m(m+1)/2} - sum_{j=0}^{[m/2]} A_{2^{m-1} - 2^{m-1-j}} }. end{equation}     

A new binary sequence family with low correlation and large size

For odd n=2l+1 and an integer /spl rho/ with 1/spl les//spl rho//spl les/l, a new family S/sub o/(/spl rho/) of binary sequences of period 2/sup n/-1 is constructed. For a given /spl rho/, S/sub o/(/spl rho/) has maximum correlation 1+2/sup n+2/spl rho/-1/2/, family size 2/sup n/spl rho//, and maximum linear span n(n+1)/2. Similarly, a new family of S/sub e/(/spl rho/) of binary sequences of period 2/sup n/-1 is also presented for even n=2l and an integer /spl rho/ with 1/spl les//spl rho/相似文献   

Generalized Kasami Sequences: The Large Set

In this correspondence, new binary sequence families F^k of period 2ⁿ-1 are constructed for even n and any k with gcd(k,n)=2 if n/2 is odd or gcd(k,n)=1 if n/2 is even. The distribution of their correlation values is completely determined. These families have maximum correlation 2^n/2+1 and family size 2^3n/2 + 2^n/2 for odd n/2 or 2^3n/2+2^n/2-1 for even n/2. The proposed families include the large set of Kasami sequences, where the k is taken as k=n/2+1.     

On the weight distribution of the coset leaders of the first-order Reed - Muller code (Corresp.)

Letalpha_{n}denote the number of cosets with minimum weightnof the(2^{m}, m + 1)Reed-Muller code. Thealpha_{n}for2^{m-2} leq n < 2^{m-2} + 2^{m - 4}is determined.     

Markov types and minimax redundancy for Markov sources

Redundancy of universal codes for a class of sources determines by how much the actual code length exceeds the optimal code length. In the minimax scenario, one designs the best code for the worst source within the class. Such minimax redundancy comes in two flavors: average minimax or worst case minimax. We study the worst case minimax redundancy of universal block codes for Markovian sources of any order. We prove that the maximal minimax redundancy for Markov sources of order r is asymptotically equal to 1/2m/sup r/(m-1)log/sub 2/n+log/sub 2/A/sub m//sup r/-(lnlnm/sup 1/(m-1)/)/lnm+o(1), where n is the length of a source sequence, m is the size of the alphabet, and A/sub m//sup r/ is an explicit constant (e.g., we find that for a binary alphabet m=2 and Markov of order r=1 the constant A/sub 2//sup 1/=16/spl middot/G/spl ap/14.655449504 where G is the Catalan number). Unlike previous attempts, we view the redundancy problem as an asymptotic evaluation of certain sums over a set of matrices representing Markov types. The enumeration of Markov types is accomplished by reducing it to counting Eulerian paths in a multigraph. In particular, we propose exact and asymptotic formulas for the number of strings of a given Markov type. All of these findings are obtained by analytic and combinatorial tools of analysis of algorithms.     

Cyclic codes over GR(4/sup m/) which are also cyclic over /spl Zopf//sub 4/

Let GR(4/sup m/) be the Galois ring of characteristic 4 and cardinality 4/sup m/, and /spl alpha/_={/spl alpha//sub 0/,/spl alpha//sub 1/,...,/spl alpha//sub m-1/} be a basis of GR(4/sup m/) over /spl Zopf//sub 4/ when we regard GR(4/sup m/) as a free /spl Zopf//sub 4/-module of rank m. Define the map d/sub /spl alpha/_/ from GR(4/sup m/)[z]/(z/sup n/-1) into /spl Zopf//sub 4/[z]/(z/sup mn/-1) by d/spl alpha/_(a(z))=/spl Sigma//sub i=0//sup m-1//spl Sigma//sub j=0//sup n-1/a/sub ij/z/sup mj+i/ where a(z)=/spl Sigma//sub j=0//sup n-1/a/sub j/z/sup j/ and a/sub j/=/spl Sigma//sub i=0//sup m-1/a/sub ij//spl alpha//sub i/, a/sub ij//spl isin//spl Zopf//sub 4/. Then, for any linear code C of length n over GR(4/sup m/), its image d/sub /spl alpha/_/(C) is a /spl Zopf//sub 4/-linear code of length mn. In this article, for n and m being odd integers, it is determined all pairs (/spl alpha/_,C) such that d/sub /spl alpha/_/(C) is /spl Zopf//sub 4/-cyclic, where /spl alpha/_ is a basis of GR(4/sup m/) over /spl Zopf//sub 4/, and C is a cyclic code of length n over GR(4/sup m/).     

A class of 1-generator quasi-cyclic codes

If R = F/sub q/[x/spl rceil/]/(x/sup m/ - 1), S = F/sub qn/[x]/(x/sup m/ - 1), we define the mapping a_(x) /spl rarr/ A(x) =/spl sigma//sub 0//sup n-1/a/sub i/(x)/spl alpha//sub i/ from R/sup n/ onto S, where (/spl alpha//sub 0/, /spl alpha//sub i/,..., /spl alpha//sub n-1/) is a basis for F/sub qn/ over F/sub q/. This carries the q-ray 1-generator quasicyclic (QC) code R a_(x) onto the code RA(x) in S whose parity-check polynomial (p.c.p.) is defined as the monic polynomial h(x) over F/sub q/ of least degree such that h(x)A(x) = 0. In the special case, where gcd(q, m) = 1 and where the prime factorizations of x/sub m/ 1 over F/sub q/ and F/sub qn/ are the same we show that there exists a one-to-one correspondence between the q-ary 1-generator quasis-cyclic codes with p.c.p. h(x) and the elements of the factor group J* /I* where J is the ideal in S with p.c.p. h(x) and I the corresponding quantity in R. We then describe an algorithm for generating the elements of J*/I*. Next, we show that if we choose a normal basis for F/sub qn/ over F/sub q/, then we can modify the aforementioned algorithm to eliminate a certain number of equivalent codes, thereby rending the algorithm more attractive from a computational point of view. Finally in Section IV, we show how to modify the above algorithm in order to generate all the binary self-dual 1-generator QC codes.