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.     

1-重量ZpZp[u]-加性码

本文定义了1-重量ZpZp[u]-加性码,其中p是奇素数.给出并证明ZpZp[u]-加性码及其对偶码之间的MacWilliams恒等式,并利用此恒等式得出1-重量加性码的对偶码最小距离的一个下界.给出1-重量加性码的结构性质.证明了在Gray映射下,1-重量ZpZp[u]-加性码的像是1-Hamming重量p-元最优线性码,达到Plotkin界和Griesmer界.最后给出1-重量ZpZp[u]-加性码的一些构造.     

几类指标为2的不可约拟循环码的重量分布

少重量线性码在认证码、结合方案以及秘密共享方案的构造中有着重要的应用。如何构造少重量线性码一直是编码理论研究的重要内容。该文通过选取特殊的定义集,构造了有限域上指标为2的不可约拟循环码,利用有限域上的高斯周期确定了几类指标为2的不可约拟循环码的重量分布,并且得到了几类2-重量线性码和3-重量线性码。结果表明,由该文构造的3类2-重量线性码中有两类是极大距离可分(MDS)码,另一类达到了Griesmer界。     

有限域上两类新的2-重量码的构造

有限域上二重量码的构造是图论、编码与密码中的重要研究课题.本文得到了有限域上两类新的2-重量码并且它们都是最优的,达到了Griesmer界.这些码由有限域的扩域上迹码的p元像定义,有阿贝尔码的代数结构,利用特征和和高斯和来计算了它们的重量分布.我们也计算了这些像码的对偶码的极小距离.最后对扩域上迹码的像在秘钥共享方案中的应用进行了刻画.     

环R+vR+v2R上线性码的MacWilliams恒等式

通过构造Gray映射,对环R+vR+v²R上线性码进行了研究.定义了环R+vR+v²R上线性码的Lee重量及其几类重量计数器,给出了环R+vR+v²R上线性码及其对偶码之间的各种重量分布的MacWilliams恒等式.利用这些恒等式,不用求出环R+vR+v²R上线性码的对偶码便可得到对偶码的各种重量分布.     

基于二次乘法特征的射影线性码

基于有限域上的二次乘法特征构造了两类线性码，精确计算出了它们的参数和重量分布.结果表明，第一类线性码是射影三重码，且对偶码关于球填充界几乎最优；第二类线性码是射影二重码，且对偶码关于球填充界几乎最优.此外，本文还得到了一些自正交码和极小码，它们可分别用于构造量子码和安全高效访问结构上的密钥共享方案.     

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。     

关于Goppa码,BCH码的广义Hamming重量

本文研究了Ｇｏｐｐａ码、ＢＣＨ码的广义Ｈａｍｍｉｎｇ重量,给出了Ｇｏｐｐａ码的广义Ｈａｍｍｉｎｇ重量的一个下界以及求该下界的一个算法;对于本原、狭义ＢＣＨ码,给出了后面一些广义Ｈａｍｍｉｎｇ重量的确切值。     

DNA Golay码的设计与分析

 DNA编码是DNA计算初始数据库中寡核苷酸序列的设计问题.合理的DNA编码可以提高实验的稳定性和正确性,从而确保DNA计算的成功率.本文给出DNA码字重量和DNA码字间Watson-Crick Hamming距离的定义;提出DNA Golay码的设计方法;分析了DNA Golay码的性质和规模;与随机搜索优码方法相比,DNA Golay码求解优码更加简单可行.     

VI-2类5维q元线性码的汉明重量谱的确定

上 线性码c的汉明重量谱为序列 ,其中,dr是c的r维子码的最小支撑重量。第VI类5维q元线性码的汉明重量谱,按照新的必要条件可以分成6个子类。运用有限射影几何方法研究VI-2类的5维q元线性码的汉明重量谱,确定VI-2类5维q元线性码的几乎所有汉明重量谱。     

基于多目标进化策略算法的DNA核酸编码设计

设计高质量的核酸分子集合能有效提高DNA计算的可靠性、有效性和可求解问题的规模。DNA分子需要满足热力学约束、相似度约束、GC含量约束等多个相互冲突的目标函数,是典型的多目标优化问题。该文提出一种多目标进化策略(MOES)算法求解DNA分子序列设计问题,算法设计了随机碱基变异算子实现高效的局部搜索和全局搜索。改进的评价函数综合考虑了候选解的支配关系和冲突目标的平衡程度,选取符合DNA编码约束的核酸序列。实验结果证明,该文提出的算法具有高效的搜索效率和快速收敛能力,可以产生高质量的DNA序列集合,优于其他对比算法产生的DNA分子序列集合。     

New construction of multiwavelength optical orthogonal codes

We investigate multiwavelength optical orthogonal codes (MWOOCs) for optical code-division multiple access. Particularly, we present a new construction method for (mn,/spl lambda/+2,/spl lambda/) MWOOCs with the number of available wavelengths m, codeword length n, and constant Hamming weight /spl lambda/+2 that have autocorrelation and cross-correlation values not exceeding /spl lambda/. In the proposed scheme, there is no constraint on the relationship between the number of available wavelengths and the codeword length, and it is also possible to use an arbitrary /spl lambda/. We show that the constructed code is optimal, especially for /spl lambda/=1. Finally, we analyze the bit error rate of the new code and compare it with that of other optical codes.     

Optical orthogonal codes with large crosscorrelation and their performance bound for asynchronous optical CDMA systems

Optical orthogonal codes (OOCs) are commonly used as signature codes for optical code-division multiple-access (OCDMA) communication systems. Many OOCs have been proposed and investigated. Asynchronous OCDMA systems using conventional OOCs have a very limited number of subscribers and few simultaneous users. Recently, we reported a new code family with large code size by relaxing the crosscorrelation constraint to 2. In this paper, by further loosening the crosscorrelation constraint, we adopt the random greedy algorithm to construct a code family which has larger code size and more simultaneous users. We also derive an upper bound of the number of simultaneous users for a given code length, code weight, and bit error rate. The study shows that it is possible to have codes approaching this bound.     

峰均功率比约束下扩展目标波形优化

针对包络约束条件下扩展目标最优检测波形设计,提出了峰均功率比约束条件下最优检测波形优化方法。首先,建立了扩展目标信号模型;然后,通过将恒定包括约束转换成峰均功率比约束,推导出该约束下扩展目标最优检测波形优化模型;并将该非凸模型转换成易于求解的凸优化模型,由此获得了恒定包络和低起伏包络条件下的最优检测波形;最后,以某典型扩展目标为例,仿真对比了不同约束参数下波形的检测性能,验证了优化所得恒定包络、低起伏包络波形相比于传统Barker 码波形具有更好的检测性能。     

Joint spatial-frequency blind multiuser detection based on LCCMA

Multicarrier code division multiple access (MC-CDMA) has the ability to combat with frequency selective fading and antenna array can enhance the performance of system. The paper proposes a novel joint spatial-frequency blind multiuser detection for antenna array MC-CDMA based on linear constraint constant modulation algorithm (LCCMA), which has robust performance and can ensue the weight vectors to converge to that of the desired user. Simulation indicates the proposed algorithm has better bit error ratio (BER) performance than that of the traditional beamforming-based two-step algorithm.     

极大等重等距码结构的再分析

本文根据文[1]提出的极大等重等距码的概念,利用等重等距码窗口矩阵设计原理,对(n,4,m)极大等重等距码结构重新进行了分析.讨论了码重基本情形,对称情形与非对称情形等几类特殊结构类型,并组合了各种不同结构的极大等重等距码,其结果比较完整地解决了(n,4,m)极大等重等距码的结构等价类问题.     

数字全息数据存储系统中的格雷映射等重调制码的设计

在数字全息数据存储系统的记录通道中,使用二进制映射等重调制码有利于信号的检测.本文作者提出了6:8格雷映射等重调制码的编码方案,将每6比特数据视为一个格雷码字,而相应的等重码设计为具有2单位距离特性.当检测到的8比特码字中发生一个2码元交换错误时,该方案具有一定的容错能力.误码性能的仿真结果表明,在系统的信噪比较低时6:8格雷映射等重调制码优于6:8二进制映射等重调制码.     

On the undetected error probability of nonlinear binary constantweight codes

The undetected error probability (UEP) of binary (n, 2δ, m) nonlinear constant weight codes over the binary symmetric channel (BSC) is investigated, where n is the blocklength, m is the weight of codeword and 2δ is the minimum distance of the codes. The distance distribution of the (n, 2, m) nonlinear constant weight codes is evaluated. It is proven in this paper that the (5, 2, 2) code, (5, 2, 3) code, (6, 2, 3) code, (7, 2, 4) code, (7, 2, 3) code and (8, 2, 4) code are the only proper error-detecting codes in the (n, 2, m) nonlinear constant weight codes for n⩾5, in the sense that their UEP is increased monotonically with the channel error rate p, of course all these proper codes are m-out-of-n codes. Furthermore, it is conjectured that except for the cases of n⩽4δ, there are no proper error-detecting binary (n, 2δ, m) nonlinear constant weight codes, for n>8 and δ⩾1     

Optical orthogonal codes with nonideal cross correlation

For optical code division multiple access (OCDMA) networks, many optical orthogonal codes (OOCs) with ideal auto- and cross-correlation properties had been studied widely. In this paper, we relax the cross-correlation constraint slightly and propose a new code family based on perfect difference codes. Given the same code weight and code length, the size of new codes may increase 10 times more than that of ideal OOCs. Although the maximum cross correlation of new codes is larger than one, the cross correlation is less than or equal to one, for the most part. Consequently, the performance of new codes approaches that of ideal OOCs. Numerical results show that the performance of proposed codes was almost the same as that of conventional OOCs under the same code length and code weight     

On asymptotic ensemble weight enumerators of LDPC-like codes

For LDPC-like codes such as LDPC, GLDPC, and DGLDPC codes, it is well known that the error floor can be caused by the codewords of small weights or stopping sets of small sizes. In this paper, we investigate the computation of asymptotic weight enumerators such that it becomes a convenient tool to determine a good distribution of code ensembles. In addition, by analyzing the first order approximation, we derive a condition to obtain a negative asymptotic growth rate of the codewords of small linear-sized weights, which is an important constraint for distribution optimization. Also the weight enumerators of turbo and repeat-accumulate codes are investigated. Furthermore, we extend our results to nonbinary DGLDPC codes. Generalization to N-layer and convolutional code based LDPC-like codes are also developed.