完全杂凑族的一个新下界

考虑(n,m,w)-完全杂凑族的下界,运用初等的方法给出一个新的下界,并给出新的下界比著名的Fredman-Komlos下界好的条件.     

基于初等变换的量子码构造

为了探讨一般量子稳定子码的简单构造方法,在满足对偶包含条件C⊥(C)C的约束下,提出了从一类量子稳定子码C= [[N,K,D]]q到量子稳定子码C'=[[N-1,K+1,D']]q的基于矩阵初等变换的构造方法.该方法的优点在于码字构造时,量子稳定子码和经典纠错码都是在Fq上进行操作,无须做Fq2到Fq上的映射转换,也无...     

FPGA-Implemented Fractal Decoder with Forward Error Correction in Short-Reach Optical Interconnects

Forward error correction (FEC) codes combined with high-order modulator formats, i.e., coded modulation (CM), are essential in optical communication networks to achieve highly efficient and reliable communication. The task of providing additional error control in the design of CM systems with high-performance requirements remains urgent. As an additional control of CM systems, we propose to use indivisible error detection codes based on a positional number system. In this work, we evaluated the indivisible code using the average probability method (APM) for the binary symmetric channel (BSC), which has the simplicity, versatility and reliability of the estimate, which is close to reality. The APM allows for evaluation and compares indivisible codes according to parameters of correct transmission, and detectable and undetectable errors. Indivisible codes allow for the end-to-end (E2E) control of the transmission and processing of information in digital systems and design devices with a regular structure and high speed. This study researched a fractal decoder device for additional error control, implemented in field-programmable gate array (FPGA) software with FEC for short-reach optical interconnects with multilevel pulse amplitude (PAM-M) modulated with Gray code mapping. Indivisible codes with natural redundancy require far fewer hardware costs to develop and implement encoding and decoding devices with a sufficiently high error detection efficiency. We achieved a reduction in hardware costs for a fractal decoder by using the fractal property of the indivisible code from 10% to 30% for different n while receiving the reciprocal of the golden ratio.     

外语教学中的出错探源与纠错

从理论上阐述了外语学习所犯错误的种类及其性质、影响，着重阐述了错误的起因及纠错手段     

循环码译码的Dixon结式方法

针对纠错码译码就是非线性方程组的求解问题,提出利用Dixon结式方法对译码方程进行消元以得到接收数据中的错位多项式.首先,根据纠错码的纠错能力和接收数据得到伴随式矩阵并通过该矩阵的秩确定接收码字中错误位的个数.然后,根据错位个数和伴随多项式构造译码方程.译码时,将其中一个错位变元作为隐藏变元,利用Dixon结式方法进行消元.最后,得到的Dixon结式就是关于隐藏变元的多项式.该多项式去掉多余因子后就是错位多项式,利用Chien搜索法即可求解出错误位置.当错位较多时,采用逐次计算结式的方法以筛除计算过程中的多余因子和重因子.另外,根据不同错位个数得到的错位多项式,提出了构造一类循环码错位多项式符号解的猜想,该猜想可以大大提高译码效率.实验验证了结式理论在纠错码译码方面的应用是有效的且有助于降低对芯片性能的要求.     

B邻接片错误定位码的译码

针对两类Ｂ邻接片错误定位码进行了分析，并给出了其译码方案．     

The density function of the number of moves to complete the Towers of Hanoi puzzle

Any sequence of legal moves leads the Towers of Hanoi puzzle to an arrangement from which the final configuration must be built up. A recursive algorithm which finishes off the puzzle is considered and, assuming a uniform distribution on the possible unfinished situations, the density function of the number of moves it takes is derived.     

纠错码在多路开关量输入通道自检中的应用

把纠错码应用于多通道遥信输入通道的故障自检．分析了多路开关量输入模板的故障类型及错码表现．比较了几种编码方案．给出编码器的电路和译码自检的软件．     

The asymptotic probability distribution of the relative distance of additive quantum codes

For given information rate R, it is proved as n tends to infinite, that almost all additive ?n,n⋅R? quantum codes (pure and impure) are the codes with their relative distance tending to h⁻¹(1−R), where is an entropy function.