一种三元线性互补对偶码与自正交码的构造方法

有限域上线性互补对偶(LCD)码有良好的相关特性和正交特性,并能够防御信道攻击。自正交码是编码理论中一类非常重要的码,可以用于构造量子纠错码。该文研究了有限域F3上的LCD码。通过选取4种合适的定义集,利用有限域F3上线性码是LCD码或自正交码的判定条件,构造了4类3元LCD码和一些自正交码,并研究了这4类线性码的对偶码,得到了一些3元最优线性码。     

一种四元厄米特LCD码与厄米特自正交码的构造方法

有限域上线性互补对偶（LCD）码具有良好的结构和性质,并在双用户加法器信道中得到了广泛的应用.自正交码是编码理论中一类重要的线性码,常被用于构造量子纠错码.本文根据有限域上线性码是厄米特LCD码或厄米特自正交码的判定条件,通过选取合适的定义集,构造出了四类四元厄米特LCD码和厄米特自正交码.同时,本文还研究了这四类线性码的厄米特对偶码,并得到了一些四元最优线性码.     

环 F2＋ uF2＋ u2 F2上的常循环码

常循环码是一类重要的纠错码,本文基于（xn －1）在 F2[x]上的分解,探讨了环 R＝ F2＋ uF2＋ u2 F2上任意长度的（1＋λu）常循环码的极小生成元集（λ为R上的单位）。通过分析该环上循环码和常循环码的置换等价性,得到了该环上码长为奇数及码长 N≡2（mod 4）时（1＋ u2）常循环码的生成多项式和极小生成元集。     

AES密码算法S盒的线性冗余研究

本文借助有限域上的迹变换,证明了有限域GF(2ⁿ)上的幂双射x^k的坐标函数的非零线性组合都线性等价,且等价变换共有2ⁿ-1个;证明了AES算法的S盒的坐标函数的非零线性组合都线性等价,且在添加0元后,本文构造的坐标函数的给定线性组合到其它线性组合的等价变换全体构成{0,1}^<em>n同构的群.本文还给出了AES算法的S盒的最低坐标函数到其它坐标函数的等价变换,它们构成了等价变换群的一组基.本文还证明了Fuller J和Millan W构造的等价变换之和都不再是坐标函数的线性组合之间的等价变换.     

有限非链环上的自对偶常循环码及其应用

纠错码是提高信息传输效率与可靠性的重要手段.构造性能良好的线性码类是纠错码研究中的一个基本问题.本文主要讨论了有限非链环F_q[v]/（v^m－v）上自对偶常循环码的代数结构,包括Euclidean自对偶常循环码、Hermitian自对偶常循环码以及Hermitian自对偶常循环码的极大距离可分（MDS）码.本文给出了环F_q[v]/（v^m－v）上常循环码是Euclidean自对偶码的充分条件,以及是Hermitian自对偶码的充要条件,并利用Gray映射构造了有限域F_q上一些参数较好的自对偶码.特别地,本文得到了有限域F_19²上一个新的参数为[16,8,6]的Hermitian自对偶码.     

基于向量空间不同访问群体的门限方案

针对具有不同访问权限的群体的秘密共享是难于处理的问题,在有限域上引入内积向量空间的概念,研究子空间的直和及其正交补结构中基向量的组成形式;利用Gram-Schmidt算法和最近向量定理设计了一个基于向量空间的（s+r, m+n）门限方案,并将此方案推广到有限多个不同访问群体的情形。结果表明,基于向量空间的不同访问群体的门限方案满足秘密共享的重构和安全性要求,是一个完备的秘密共享方案。     

指数积序列的构造与性质

本文给出了一种能在微机上快速生成的有限域F(2~m)的密码序列,它是由在及(2~m)上两个m序列经指数积运算得到的,所以称为指数积序列。本文证明了它的周期是(2~(mM)-l)·(2~mM-1),线性复杂度是M+N+[(M+1)~m-1][(N+1)~m-1]-W~mN-N~mM,其中M、N是所用到的两个m序列的级数。     

有限域上傅立叶变换的一种新的快速算法

本文提出了一种计算任意有限域GF(P~m)上n=P~m-1点傅立叶变换的快速算法。其运算规则,适于串行流水处理,GF(P~m)上乘和加运算量都是O(n log~2n),在某些域上乘法可减到O(n log n)。文中给出了此算法的流图和硬件实现框图,并估计了其运算量和硬件实现速度。这种算法对于利用谱技术进行纠错码的编译码有重要的意义,也可用于有限域上多项式的快速求值。     

经典逻辑度量空间中的模2次范整线性空间结构

 将次范整线性空间理论用于研究经典逻辑度量空间([F(S)],ρ).构造出了([F(S)],ρ)中的一类等距变换,证明了这类等距变换之集构成一个群;进而证明了经典逻辑度量空间([F(S)],ρ)相对于此结构构成带有模2加法性质的次范整线性空间,且此空间同构于有限域F(2)上的线性赋范空间;建立了范数与逻辑公式的真度以及范数与逻辑度量空间中的度量ρ之间的关系.     

基于线性分组码的(k,n)门限方案的研究

首先探讨了纠错码与（k，n）门限方案间的内在联系，然后分析了（n，k）MDS码用于构造（k，n）门限方案的充要条件及具体方法；给出了纠错码门限方案的几个重要定理和构造（k，n）门限方案的方法。     

Nonintersecting subspaces based on finite alphabets

Two subspaces of a vector space are here called "nonintersecting" if they meet only in the zero vector. Motivated by the design of noncoherent multiple-antenna communications systems, we consider the following question. How many pairwise nonintersecting M/sub t/-dimensional subspaces of an m-dimensional vector space V over a field F can be found, if the generator matrices for the subspaces may contain only symbols from a given finite alphabet A/spl sube/F? The most important case is when F is the field of complex numbers C; then M/sub t/ is the number of antennas. If A=F=GF(q) it is shown that the number of nonintersecting subspaces is at most (q/sup m/-1)/(q/sup Mt/-1), and that this bound can be attained if and only if m is divisible by M/sub t/. Furthermore, these subspaces remain nonintersecting when "lifted" to the complex field. It follows that the finite field case is essentially completely solved. In the case when F=C only the case M/sub t/=2 is considered. It is shown that if A is a PSK-configuration, consisting of the 2/sup r/ complex roots of unity, the number of nonintersecting planes is at least 2/sup r(m-2)/ and at most 2/sup r(m-1)-1/ (the lower bound may in fact be the best that can be achieved).     

基于恒模算法的天线阵多载波码分多址系统空频盲多用户检测

多载波码分多址(MC-CDMA)可以对抗频率选择性,天线阵可以提高系统的性能.本文首先提出一种基于恒模算法的天线阵MC-CDMA系统空频盲自适应多用户检测,该算法具有MN维权向量,结构相对复杂;进而提出一种空频联合约束恒模算法的盲自适应多用户检测,可以保证算法具有鲁棒性,收敛于期望用户,该算法具有M N权向量,结构简单.仿真表明,本文提出的算法比传统的基于波束成形的两步算法具有更好的误码率性能.     

1×1024位敏光电探测器件性能和应用研究

主要介绍由半导体、电真空和计算机技术相结合研制而成的 1× 10 2 4位敏光电探测器件的基本原理、结构设计、性能参数和应用等。该器件采用紫外光电阴极、Z型 MCP、1× 10 2 4线列阳极编码和 6 6根引出线输出的结构 ,其输出信号经放大、解码、计算机存储等处理 ,在显示器上显示。可探测低至 10 -13 W的紫外光信号 ,且具有较好的时间和空间分辨率     

How does a porcupine separate its quills?

Sets of unit vectors inN-dimensional Euclidean vector space whose constituent vectors are separated one from another by at least a fixed distanced, prescribed once for all and independent ofN, are of interest in theory and practice; they have fondly been called "porcupine codes." Although an elegant constructive proof of Gilbert shows that the number of vectors in a porcupine code (of givend) can increase exponentially withN, no systematic method is yet known for generating porcupine codes of this cardinality. Corresponding to a collection ofMvectors, we can partition the space into maximum-likelihood regions, thejth of which consists of those vectors that lie closer to thejth than to any other element of the collection. Each maximum-likelihood region is bounded by at most(M - 1)hyperplanes, and we denote byKthe total number of these bounding hyperplanes. Collections for whichKis small may be expected to have greater symmetry than those for whichKis large. In this paper we show that, for porcupine codes,K geq (M/2)^{1/s}, withsdepending only ond, the minimum separation of the code vectors. Hence, for the number of vectors of a porcupine code to increase exponentially with dimension, the number of separating hyperplanes must do so as well. We conclude with, an application to the permutation codes introduced by Slepian, showing that the number of vectors of a porcupine code which is of permutation-modulation type can not increase exponentially withN.     

SER of M-ary NCFSK with S + N Selection Combining in Nakagami Fading for Integer m

The performance of M-ary orthogonal noncoherent frequency-shift keying (NCFSK) with N branch signal-plus-noise (S + N) selection combining (SC) in Nakagami-m fading (m, integer) is studied. Both independent, identically distributed (i.i.d) and independent, nonidentically distributed (i.n.d) diversity branches are considered and two S + N SC receiver structures are examined. The performances of the S + N SC receivers are compared to those of classical SC and square-law combining (SLC) receivers. The effects of modulation order, fading parameter and the number of diversity branches on the performance of S + N SC are compared to the effects on the performances of classical SC and SLC. For example, it is shown that in an i.n.d fading channel, the value of signal-to-noise ratio (SNR) at which the error rate curves of classical SC and S + N SC cross, decreases as the modulation order, M, increases. Our results indicate that in i.n.d fading channels classical SC outperforms S + N SC for small ranges of SNR, while for moderate to large SNR values S + N SC has superior performance over classical SC. It is also shown that increasing the diversity order will increase the performance gap of S 4N SC over classical SC and over SLC in both i.i.d and i.n.d Nakagami-m fading channels     

用于超宽带高分辨率成像的二维稀疏MIMO面阵拓扑结构研究

分析并总结了超宽带二维多输入多输出(Multiple Input Multiple Output, MIMO)面阵拓扑结构设计的两条原则——等效孔径的均匀性与无明显遮蔽性, 并根据这两条原则提出了一种用于超宽带近距离高分辨率成像的新型面阵拓扑结构.与尺寸、阵元数相同的MIMO面阵相比, 该新型面阵结构在仿真获取的方向图中具有更好的聚焦效果和旁瓣抑制能力.并且, 不同距离下的聚焦结果显示, 该面阵的峰值旁瓣水平均要低于另两个阵列2 dB以上.对复杂目标成像的实验结果进一步证明了该阵列良好的成像性能.结合其等效阵元数量较少的特点, 文中提出的这种新型MIMO面阵拓扑结构为高效、实时的超宽带近距离高分辨率成像应用提供了可能.     

电磁矢量传感器及其阵列累量域虚拟导向矢量的线性无关度

通过研究多个导向矢量之间的线性无关性讨论电磁矢量传感器及其阵列累量域观测的唯一性问题。导出了累量域电磁矢量传感器及其阵列线性无关虚拟导向矢量个数的上界和下界。这些结论对确定电磁矢量传感器及其阵列累量域可分辨非高斯信号源个数具有一定的参考价值。给出的仿真实验结果验证了文中的分析和推导。     

Nondirect convergence radius and number of iterations of theHopfield associative memory

Considers a Hopfield associative memory consisting of n neurons, designed to store an m-set of n-dimensional ±1 statistically independent uniformly distributed random vectors (fundamental memories), using a connection matrix, constructed by the usual Hebbian rule. Previous results have indicated that the maximal value of m, such that almost all m vectors are stable points of the memory, in probability (i.e., with probability approaching one as n approaches infinity), is n/(2 log n)(n/(4 log n) if all m vectors must be stable simultaneously, in probability). Previous work further analyzed the direct convergence (i.e., convergence in one iteration) error-correcting power of the Hopfield memory. The present authors rigorously analyze the general case of nondirect convergence, and prove that in the m=n/(2 log n) case, independently of the operation mode used (synchronous or asynchronous), almost all memories have an attraction radius of size n/2 around them (in the n/(4 log n) case, all memories have such an attraction radius, in probability). This result, which was conjectured in the past but was never proved rigorously, combined with an old converse result that the network cannot store more than n/(2 log n)(n/(4 log n)) fundamental memories, gives a full picture of the error-correcting power of the Hebbian Hopfield network. The authors also upper bound the number of iterations required to achieve convergence     

一种优化非均匀阵列天线测向性能的方法

本论文给出了一种新的优化非均匀天线阵列阵元排布的方法阵元微调法。非均匀阵列天线具有许多均匀阵列天线不具备的优点,可以在节省设备量的同时增加天线孔径,但是利用非均匀阵列天线测向时也容易产生估计模糊。解决非均匀阵列天线估计模糊问题的途径之一就是调整天线阵列的排布。计算机仿真证实,经过微调法优化的非均匀阵列的测向性能有很大改善。     

环F4+uF4上线性码及其对偶码的Gray象

研究了环F4+uF4与域F4上的线性码,利用环F4+uF4上码C的Gray重量wG,Gray距离d G和(F4+uF4)n到F4 2n的Gray映射φ,证明了环F4+uF4上线性码C及其对偶码的Gray像φ(C)为F4上的线性码和对偶且dH G(φ(C))dG(C)。同时,给出了F4+uF4上循环码C的Gray像φ(C)为F4上的2-拟循环码。