A New Scheme to Determine the Weight Distributions of Binary Extended Quadratic Residue Codes

This letter proposes a novel scheme which consists of a weight-counting algorithm, the combinatorial designs of the Assmus-Mattson theorem, and the weight polynomial of Gleason?s theorem to determine the weight distributions of binary extended quadratic residue codes. As a consequence, the weight distributions of binary (138, 69, 22) and (168, 84, 24) extended quadratic residue codes are given.     

Theoretical Analysis of Bit-Error Probability for Convolutional Codes with Weight Enumerators

The paper introduces the state reduction algorithm and accelerated state reduction algorithm are used to compute the distance weight enumerator(transfer function)T[x,y] of convolutional codes.Next use computer simulation to compare upper bound on the bit error probability on an additive white Gaussian noise(AWGN) for maximum free distance(MFD) codes of previously found and optimum distance spectrum(ODS) codes with rate 1/4,overall constraint length are 5 and 7,respectively.Finally,a method of how to search for good convolutional codes is given.     

Heuristic Algorithms for Constructing Binary Constant Weight Codes

Constant weight binary codes are used in a number of applications. Constructions based on mathematical structure are known for many codes. However, heuristic constructions unrelated to any mathematical structure can become of greater importance when the parameters of the code are larger. This paper considers the problem of finding constant weight codes with the maximum number of codewords from a purely algorithmic perspective. A set of heuristic and metaheuristic methods is presented and developed into a variable neighborhood search framework. The proposed method is applied to 383 previously studied cases with lengths between 29 and 63. For these cases it generates 153 new codes, with significantly increased numbers of codewords in comparison with existing constructions. For 10 of these new codes the number of codewords meets a known upper bound, and so these 10 codes are optimal. As well as the ability to generate new best codes, the approach has the advantage that it is a single method capable of addressing many sets of parameters in a uniform way.     

关于等重码不可检错误概率的界

本文研究了二元等重码不可检错误概率(UEP)的界.首先,我们通过研究二元等重码的对偶距离分布及其性质,给出二元等重码UEP的一个新的下界,该下界改进了Fu-Kl  ve-Wei的最新结果;然后,我们指出2003年Fu-Kl  ve-Wei关于二元等重码UEP上界的某些结果有错误,我们随后给出更正后的结果,即二元等重码UEP的平均值和一个上界.     

再论二元非线性等重码的检错性能

本文利用对偶距离分布的性质,从理论上证明了文「４」的必要条件在δ＝１时实际上是充分条件,并得出对于（ｎ,２,ω）码,最佳检错码与检错好码是等价的,最后,本文讨论了（ｎ,２,ω）码不可检错误概率的界。     

一种构造GC常重量DNA码的方法

GC重量是DNA码的一个重要参数,如何构造满足GC常重量约束的DNA码是一个有趣的问题。该文通过在DNA码与四元码之间建立一个双射,将构造满足GC常重量约束的DNA码转化为构造GC常重量四元码。通过代数的方法,构造了3类满足GC常重量约束的DNA码。     

Determination of the Local Weight Distribution of Binary Linear Block Codes

Some methods to determine the local weight distribution of binary linear codes are presented. Two approaches are studied: A computational approach and a theoretical approach. For the computational approach, an algorithm for computing the local weight distribution of codes using the automorphism group of the codes is devised. In this algorithm, a code is considered the set of cosets of a subcode, and the set of cosets is partitioned into equivalence classes. Thus, only the weight distributions of zero neighbors for each representative coset of equivalence classes are computed. For the theoretical approach, relations between the local weight distribution of a code, its extended code, and its even weight subcode are studied. As a result, the local weight distributions of some of the extended primitive Bose-Chaudhuri-Hocquenghen (BCH) codes, Reed-Muller codes, primitive BCH codes, punctured Reed-Muller codes, and even weight subcodes of primitive BCH codes and punctured Reed-Muller codes are determined     

关于二元等重码的最大码字数

本文利用Johnson Schemes理论研究了二元等重码及其最大码字数问题.在Delsarte的associate schemes理论中,Q-变换被引入以研究二元等重码的距离分布.首先,本文研究了等重码距离分布的Q-变换;然后,通过使用Q-变换的性质,我们研究了二元等重码的最大码字数问题并得到码字数的一个新的上界,该上界在形式上类似于纠错码理论中的Grey-Rankin界,并且在某些情况下优于已知的结果.     

A Decomposition Theory for Binary Linear Codes

The decomposition theory of matroids initiated by Paul Seymour in the 1980s has had an enormous impact on research in matroid theory. This theory, when applied to matrices over the binary field, yields a powerful decomposition theory for binary linear codes. In this paper, we give an overview of this code decomposition theory, and discuss some of its implications in the context of the recently discovered formulation of maximum-likelihood (ML) decoding of a binary linear code over a binary-input discrete memoryless channel as a linear programming problem. We translate matroid-theoretic results of Grotschel and Truemper from the combinatorial optimization literature to give examples of nontrivial families of codes for which the ML decoding problem can be solved in time polynomial in the length of the code. One such family is that consisting of codes for which the codeword polytope is identical to the Koetter-Vontobel fundamental polytope derived from the entire dual code C^perp. However, we also show that such families of codes are not good in a coding-theoretic sense-either their dimension or their minimum distance must grow sublinearly with code length. As a consequence, we have that decoding by linear programming, when applied to good codes, cannot avoid failing occasionally due to the presence of pseudocode words.     

A Unified Approach to the Construction of Binary and Nonbinary Quasi-Cyclic LDPC Codes Based on Finite Fields

A unified approach for constructing binary and nonbinary quasi-cyclic LDPC codes under a single framework is presented. Six classes of binary and nonbinary quasi-cyclic LDPC codes are constructed based on primitive elements, additive subgroups, and cyclic subgroups of finite fields. Numerical results show that the codes constructed perform well over the AWGN channel with iterative decoding.     

BHQRSM: Binary Hex Quadratic Residue Security Model to Enhance the Trust in MANETs

Mobile adhoc network (MANET) possesses various security challenges mainly due to its varying network topology. As central coordination is not possible in MANETs, sharing of keys between nodes is a difficult task. In this paper, we present a Binary Hex Quadratic Residue Security Model that does not require any kind of key distribution between the nodes in MANETs. We use a stream of equal weighted hex codes of decimal numbers and Ex-OR operations to generate a security vector which facilitates matching of code words and also determine the active and malicious nodes in the network. Our approach also saves energy as it requires less computational analysis when compared to existing approaches. We validate our approach through simulations results.     

一种二进制算术码的软解码算法

算术码是一种高效率的熵编码方法,广泛应用在多媒体压缩中.但是,算术码的高压缩性能也导致其对信道传输中残存的误码极其敏感,存在误码扩散现象.本文将算术码解码过程表示为一个有限状态机(FSM),利用最大后验概率估计准则(MAP)进行序列解码,FSM提供先验信息估计和差错检测功能.通过对独立信源和JPEG2000编码图像的实验表明,该解码算法降低了二进制算术码的序列差错率,提高了解压缩图像的质量.     

环Fp+vFp+v2Fp上线性码的各种重量计数器及其MacWilliams恒等式

首先给出了环R=F_p+vF_p+v²F_p上线性码及其对偶码的结构及其Gray象的性质.定义了环R上线性码的各种重量计数器并讨论了它们之间的关系,特别的,确定了该环上线性码与其对偶码之间关于完全重量计数器的MacWilliams恒等式,利用该恒等式,进一步建立了该环上线性码与其对偶码之间的一种对称形式的MacWilliams恒等式.最后,利用该对称形式的MacWilliams恒等式得到了该环上的Hamming重量计数器和Lee重量计数器的MacWilliams恒等式,利用不同的方法推广了文献[7]中的结果.     

A Low Complexity Decoding Algorithm for Extended Turbo Product Codes

In this letter, we propose a low complexity algorithm for extended turbo product codes by considering both the encoding and decoding aspects. For the encoding part, a new encoding scheme is presented for which the operations of looking up and fetching error patterns are no longer necessary, and thus the lookup table can be omitted. For the decoder, a new algorithm is proposed to extract the extrinsic information and reduce the redundancy. This new algorithm can reduce decoding complexity greatly and enhance the performance of the decoder. Simulation results are presented to show the effectiveness of the proposed scheme.     

基于组合赋权法的指标权重确定方法研究与应用

指标权重确定是作战决策过程中的一个重要环节,直接影响着作战决策的可靠性和正确性.针对有效进行指标权重确定的现实需求,研究了主观赋权法和客观赋权法相结合的权重确定方法.首先,在分析主观赋权法和客观赋权法各自特点的基础上,提出了两者结合使用的思想;其次,研究了运用最小二乘原理求解组合权重的基本步骤,给出了具体算法;最后,通过算例,得到了与事实相符的结论,验证了所用方法的有效性.     

基于粗糙集的电力通信网综合权重确定方法

提出了利用粗糙集的属性依赖度判断指标重要性的方法。该方法不需要建立解析式的教学模型,完全由数据驱动来确定各指标的权值,克服了传统权值确定方法的主观性影响,使评估结果更可靠。在此基础上,结合主观赋权方法,提出了一种兼顾主观偏好和客观数据信息的综合权重确定方法。对电力通信网光纤保护通道各指标的权重确定结果表明该方法有效的避免了传统定权方法的不足,提高了评估的准确性和合理性。     

任意概率分布下Golomb码和扩展Gamma码的性能分析

以信源的平均值给出了任意概率分布下Golomb码的平均码长的上下界和最优的参数选择准则。在Golomb码的基础上,进一步推广了Elias的码,提出了扩展的码,同时给出了其性能界和最优的参数选择准则。扩展码是一类通用码,而且在一定的条件下可以达到渐近最优的性能。最后,提出了一个低复杂性的基于Golomb码和扩展码的通用数据压缩框架,并通过构建一个样例系统说明了该数据压缩框架的实际应用价值。     

On the Number of Inequivalent Binary Self-Orthogonal Codes

Let Psi_k,n denote the number of inequivalent binary self-orthogonal [n, k] codes. We present a method which allows us to compute Psi_k,n explicitly for a moderate k and an arbitrary n. Included in this paper are explicit formulas for Psi_k,n with k les 5.     

一种构造BCM码的新方法

由Imai与Hirakawa提出的多级编码方法,可用来构造具有任意大最小平方欧氏距离的分组调制(BCM)码.一个BCM码的性能主要取决于构成它的各个成分码,恰当地选择成分码是构造一个好的BCM码的关键.文章给出了一种新方法,通过选用不同长度的成分码来构造BCM码.仿真结果表明用此方法构造出的BCM码较传统的BCM码在性能与复杂度上有明显的改善.