三角多项式内插及其应用

讨论了三角多项式内插基函数的若干性质，当取样点具有特殊分布时，采用三角多项式内插法可精确重构原周期带限信号。给出了用于有限样点和加密的内插公式。     

重根循环码的周期分布和广义周期分布

近几年来，重根循环码再度引起人们的重视，本文在文「１」的基础报重根循环码的周期２分布和广义周期分布，给出了通用的计算方法和计算公式，并确定了某些重根循环码的周期分布和广义周期分布。     

再论循环码的周期分布

本文揭示了循环码的周期分布与其对偶码的周期分布的关系，给出了一般循环码及其对偶码内无内周期码字的精确计数公式。     

缩扩生成器的构造与分析

论文将自扩生成器与缩减生成器组合构成了一种新型的伪随机序列生成器——缩扩生成器，它由两个三元的线性反馈移位寄存器（LFSR）构成。文中讨论了某种特殊情形下得到的缩扩序列的周期、符号分布、特征多项式等密码学性质。     

同轴波纹波导的高频特性数值分析

本文提出先用时域有限差分法计算含周期慢波结构的谐振腔的谐振频率和谐振场分布,再基于周期慢波电路色散关系的周期性质,由几个特殊色散点处的频率及波数数值组合出周期慢波线的完整色散关系的新方法。数值计算了同轴波纹波导中ＴＭ０ｎ模式的色散关系、耦合阻抗等特性参量。     

循环码的周期分布的新的计算公式

本文在［１］文的基础上进一步分析了循环码的周期分布的性质，给出了新的计算方法和公式，并且确定了一些熟知的循环码的周期分布。     

纠错码的周期分布

本文首先给出了(n,k,d)纠错码的周期分布{P_i:1≤i≤n}概念和它的实际背景,接着求出了R-S码,扩充R-S码和一般循环码的周期分布精确公式。非循环码的周期分布问题还有待进一步研究。     

同轴波纹波导的高频特性数值分析

本文提出先用时域有限差分法计算含周期慢波结构的谐振腔的谐振频率和谐振场分布,再基于周期慢波电路色散关系的周期性质,由几个特殊色散点处的频率及波数数值组合出周期慢波线的完整色散关系的新方法。数值计算了同轴波纹波导中TM0n模式的色散关系、耦合阻抗等特性参量。     

一类推广的二元Legendre-Sidelnikov序列的自相关分布

推广的Legendre-Sidelnikov序列较之原序列有更好的平衡性质,但是关于该序列的周期自相关函数,迄今仅知道一些特殊移位的情形。该文利用有限域上特征和的相关性质,给出了推广的二元Legendre-Sidelnikov序列的自相关函数的完整分布。结果表明当p3(mod 4)且qp 时,推广的Legendre-Sidelnikov序列较之原序列有更好的周期自相关函数的分布。     

布拉格光纤光传输特性研究

研究了布拉格光纤结构对光传输特性的影响。对等周期结构的径向分布、高低折射率径向包层分布和准周期径向分布等布拉格光纤结构建立了光子晶体光纤仿真软件，对光场振幅三维分布、轴向传输流分布以及径向包层数对传输特性的影响进行了计算机仿真研究，研究结果对布拉格光子晶体光纤的实际加工具有重要的参考意义。     

An approximation to the weight distribution of binary linear codes

Binary primitive BCH codes form a large class of powerful error-correcting codes. The weight distributions of primitive BCH codes are unknown except for some special classes, such as the single, double, triple error-correcting codes and some very low-rate primitive BCH codes. However, asymptotic results for the weight distribution of a large subclass of primitive BCH codes have been derived by Sidel'nikov. These results provide some insight into the weight structure of primitive BCH codes. Sidel'nikov's approach is improved and applied to the weight distribution of any binary linear block code. Then Sidel'nikov's results on the weight distributions of binary primitive BCH codes are improved and it is shown that the weights of a binary primitive code have approximate binomial distribution.     

一种非规则卷积低密度校验码的构造和短环去除方法

该文研究了使用为分组低密度校验(Low-Density Parity-Check,LDPC)码优化的度序列分布来构造卷积低密度(Low-Density Convolutional,LDC)码的方法,详细讨论了LDC码的编码、译码和短环的消除算法,实验结果说明用为分组LDPC码优化的非规则度序列分布所构造的LDC码,其性能要优于目前文献上提出的规则(homogeneous)LDC码。     

On the computation of the probability of post-decoding error events for block codes (Corresp.)

The computation of the probability of certain post-decoding error events is formulated for block codes whose weight distributions are known. A bounded-distance decoder for group codes is assumed. Numerical examples included show post-decoding character error rates for the Golay code and for some Reed-Solomon codes and the distribution of post-decoding errors for the same Reed-Solomon codes. An extension to errors and erasures decoding is also given.     

关于几类线性分组码网格图复杂度的研究

本文研究了几类线性分组码C[n,k,d]的网格图复杂度s（C）。给出并证明了码长为奇数的两类线性分组码的网格图复杂度。同时得出了有关可纠t个错的本原BCH码[2^m-1,2^m-1-mt]及其扩展本在BCH码的网格图复杂度的若干结论。从而避免了必须先寻找码的直和结构才可得到码的网格图复杂度的较好上界。     

On multilevel block modulation codes

The multilevel technique for combining block coding and modulation is investigated. A general formulation is presented for multilevel modulation codes in terms of component codes with appropriate distance measures. A specific method for constructing multilevel block modulation codes with interdependency among component codes is proposed. Given a multilevel block modulation code C with no interdependency among the binary component codes, the proposed method gives a multilevel block modulation code C' that has the same rate as C, a minimum squared Euclidean distance not less than that of C, a trellis diagram with the same number of states as that of C, and a smaller number of nearest neighbor codewords than that of C . Finally, a technique is presented for analyzing the error performance of block modulation codes for an additive white Gaussian noise (AWGN) channel based on soft-decision maximum likelihood decoding. Error probabilities of some specific codes are evaluated by simulation and upper bounds based on their Euclidean weight distributions     

Exact Probabilistic Analysis of Memoryless Combiners

Exact analytical expressions for various probability distributions in a type of stream ciphers known as memoryless combiners are derived. They relate to arbitrary linear functions and subvectors of output bits as well as to arbitrary linear functions and subvectors of input bits when the output sequence is assumed to be given. Practical approximations to the exact expressions to be used in one-step and iterative fast correlation attacks and statistical distinguishers are proposed. More generally, the results also apply to arbitrary binary linear codes that are nonlinearly transformed by time-variant Boolean functions. For comparison, the corresponding probability distributions for linear block codes on a memoryless time-variant binary symmetric channel are also determined and some practical consequences pointed out.     

Fast performance estimation of block codes

Importance sampling is used in this paper to address the classical yet important problem of performance estimation of block codes. Simulation distributions that comprise discrete- and continuous-mixture probability densities are motivated and used for this application. These mixtures are employed in concert with the so-called g-method, which is a conditional importance sampling technique that more effectively exploits knowledge of underlying input distributions. For performance estimation, the emphasis is on bit by bit maximum a-posteriori probability decoding, but message passing algorithms for certain codes have also been investigated. Considered here are single parity check codes, multidimensional product codes, and briefly, low-density parity-check codes. Several error rate results are presented for these various codes, together with performances of the simulation techniques.     

On the decoder error probability of block codes

By using coding and combinational techniques, an explicit formula is derived which enumerates the complete weight distribution of decodable words of block codes using partially known weight distributions. Also, an approximation formula for nonbinary block codes is obtained. These results give exact and approximate expressions for the decoder error probability P_E(u) of block codes     

On binary images of shortened cyclic (8, 5) codes over GF(2/sup 8/)

We have generated binary images of a large number of shortened cyclic (8, 5) codes over GF(2/sup 8/) and have computed weight distributions of the binary images of the codes. Based on the weight distributions, we have chosen four codes with the largest minimum weight 8 and the second largest minimum weight 7 among the generated codes. Over an additive white Gaussian noise channel with binary phase-shift keying modulation, simulation results have shown that block error rates of the chosen codes by a soft-decision decoding based on order-2 reprocessing are smaller than those of (64, 40) subcodes of Reed-Muller (64, 42) code by maximum likelihood decoding.     

Optimum cycle redundancy-check codes with 16-bit redundancy

Optimal binary cyclic redundancy-check codes with 16 parity bits (CRC-16 codes) are presented and compared to those in existing standards for minimum-distance, undetected-error probability on binary symmetric channels (BSCs) and properness. The codes in several cases are seen to be superior at block lengths of practical interest when they are used on low-noise BSCs. The optimum minimum distance obtainable by some CRC-16 codes is determined for all block lengths. For several typical low-noise BSCs the minimum undetected error probability achievable with some CRC-16 codes is given for all block lengths