移动信道三状态Markov模型建立及其差错序列的计算机软件产生

提出了一个建立在简单分群的 Markov 模型基础上表示移动信道的三状态Markov 模型,利用非线性最小二乘拟合法求得了此模型的解析表达式,并计算出描述模型的概率转移矩降 P。根据此模型给出的参数,用计算机软件实现方法产生出描述移动信道长突发错误特性的信道差错序列{e_(?)}。模拟结果表明,用三状态 Markov 模型表示移动信道比用 GEC 模型表示移动信道具有更高的精度,而且比一般分群的 Markov 模型更简单、实用。     

Goppa码一致校验位数目的下限

给定一个Ｇｏｐｐａ码，如何求出它的一致校验位数目问题，至今尚未解决。估计一致校验位数目，一般只用上限来估计．本文提出了不仅可用上限也可用下限来估计一致校验位数目的观点，并且给出了估计方法。用这种方法，某些特殊的Ｇｏｐｐａ码是能够求出它的一致校验位数目的。     

Quantum computation with Turaev-Viro codes

For a 3-manifold with triangulated boundary, the Turaev-Viro topological invariant can be interpreted as a quantum error-correcting code. The code has local stabilizers, identified by Levin and Wen, on a qudit lattice. Kitaev’s toric code arises as a special case. The toric code corresponds to an abelian anyon model, and therefore requires out-of-code operations to obtain universal quantum computation. In contrast, for many categories, such as the Fibonacci category, the Turaev-Viro code realizes a non-abelian anyon model. A universal set of fault-tolerant operations can be implemented by deforming the code with local gates, in order to implement anyon braiding. We identify the anyons in the code space, and present schemes for initialization, computation and measurement. This provides a family of constructions for fault-tolerant quantum computation that are closely related to topological quantum computation, but for which the fault tolerance is implemented in software rather than coming from a physical medium.     

纠错组码的一个界

给出了完全多部图覆盖与纠错组码的一种一一对应关系，从而利用Huang（1996）的一个结果给出了纠错组码的一个界，并利用仿射设计给出了使这个界的等号成立的一族线性码．     

使用除法算法对里德-所罗门编码进行解码

里德-所罗门编码是最广泛使用的纠错码之一.介绍一种使用除法算法的解码方法,发展该算法的理论并讨论支持该算法的例子.最后,证明与该解码算法有关的一个概率上的定理,关于何时该方法是最有效的,得出一些概率上的结果.     

对角量子信道的纠错码空间的存在性与构造

通过量子信道的Kraus算子,提出了对角量子信道的概念,证明了对角量子信道的一些性质：一个量子信道成为对角量子信道的充要条件是所有对角矩阵都是它的不动点;同一对角量子信道的所有压缩矩阵具有相同的秩;一个对角量子信道不可纠错的充要条件是其压缩矩阵是行满秩的.进而证明了一个对角量子信道在整个空间上可纠错当且仅当其压缩矩阵为1秩阵.最后,利用一个具体例子给出了构造对角量子信道的码空间的一种方法.     

Cryptanalysis of the Wu–Dawson Public Key Cryptosystem

A new public key cryptosystem was introduced by Wu and Dawson at the Fourth International Conference on Finite Fields (Fq4). This scheme is similar to the McEliece public key cryptosystem, in the sense that it also can be described in terms of linear error-correcting codes over finite fields. However, in contrast to the McEliece scheme, the security of the Wu–Dawson system is not based on a decoding problem which is assumed to be intractable but on the theory of generalized inverses of matrices over finite fields. The authors compare their scheme with the McEliece scheme and claim that the same level of security can be obtained using smaller codes, therefore reducing the key size. In this note it will be shown that the Wu–Dawson scheme is insecure, i.e., a trapdoor can be computed efficiently from the knowledge of the public key.     

Algebraic geometric codes with applications

The theory of linear error-correcting codes from algebraic geometric curves (algebraic geometric (AG) codes or geometric Goppa codes) has been well-developed since the work of Goppa and Tsfasman, Vladut, and Zink in 1981–1982. In this paper we introduce to readers some recent progress in algebraic geometric codes and their applications in quantum error-correcting codes, secure multi-party computation and the construction of good binary codes.      

软开关PWM变换器非线性控制新策略的研究

提出了一种基于单周控制基础上的PWM变换器非线性控制新方案.通过对积分器初始复位电压及输入基准电压的修正,克服了单周控制存在的不足,提高了对开关误差的校正能力,基本消除稳态误差.理论分析和仿真试验都证明了方案的可行性.