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1.
 In [1], Homma-Kim-Yoo showed that a code C such that the support of the associated projective system is a union of two linear subspaces, is uniquely determined up to equivalence by its weight enumerator. Let W C (z) be the weight enumerator of a code C. Assuming certain conditions on the coefficients of W C (z) for some range, we prove that the support of the associated projective system is a union of two linear subspaces. Received: February 27, 2002; revised version: October 2, 2002 Keywords: Linear code, Projective system, Weight enumerator. MSC2000: 94B27, 94B65, 51E20 Partially supported by Grant-in-Aid for Scientific Research, Ministry of Education, #12640180  相似文献   

2.
The Main Conjecture on maximum distance separable (MDS) codes states that, except for some special cases, the maximum length of a q-ary linear MDS code of is q+1. This conjecture does not hold true for near maximum distance separable codes because of the existence of q-ary near-MDS elliptic codes having length bigger than q+1. An interesting related question is whether a near-MDS elliptic code may be extended to a longer near-MDS code. In this paper we prove some non-extendibility results for certain near-MDS elliptic codes.  相似文献   

3.
We prove that, for semi-invertible linear cocycles, Oseledets subspaces associated to ergodic measures may be approximated by Oseledets subspaces associated to periodic points.  相似文献   

4.
Solving linear equations and finding eigenvalues are essential tasks in many simulations for engineering applications, but these tasks often cause performance bottlenecks. In this work, the hierarchical subspace evolution method (HiSEM), a hierarchical iteration framework for solving scientific computing problems with solution locality, is proposed. In HiSEM, the original problem is converted to a corresponding minimization function. The problem is decomposed into a series of subsystems. Subspaces and their weights are established for the subsystems and evolve in each iteration. The subspaces are calculated based on local equations and knowledge of physical problems. A small-scale minimization problem determines the weights of the subspaces. The solution system can be hierarchically established based on the subspaces. As the iterations continue, the degrees of freedom gradually converge to an accurate solution. Two parallel algorithms are derived from HiSEM. One algorithm is designed for symmetric positive definite linear equations, and the other is designed for generalized eigenvalue problems. The linear solver and eigensolver performance is evaluated using a series of benchmarks and a tower model with a complex topology. Algorithms derived from HiSEM can solve a super large-scale problem with high performance and good scalability.  相似文献   

5.
Recently Niederreiter described a new method for factoring polynomials over finite fields. As with the Berlekamp technique, the method requires the construction of a linear subspace whose dimension is precisely the number of irreducible factors of the polynomial being considered. This paper explores the connection between these subspaces and gives a characterization of other subspaces having properties which are similar.  相似文献   

6.
线性隐写码的性质与构造   总被引:1,自引:0,他引:1  
本文从隐写术的安全性需求出发抽象出一个新的编码问题,称之为隐写码。利用线性空间的直和分解得到了一种线性隐写码的构造方法。通过引入线性空间t阶维数的概念将线性隐写码问题转化成了一个代数问题,从而得到了线性隐写码长度的上界,并由此定义了最大长度可嵌入码。证明了线性最大长度可嵌入码与线性完备纠错码有1-1对应关系。  相似文献   

7.
Phillips RL  Andrews LC 《Applied optics》1983,22(23):3833-3836
Atmospheric turbulence causes random fading in any open-air optical communication channel. When the transmitted message is in the form of a block code, a binary union decoding system consisting of one storage register can be used to enhance the reliability of this type of fading channel. To illustrate the effectiveness of the binary union decoder, we compare probabilities of detecting one word out of N + 1 received words for both a binary union decoder and a simple word recognition decoder system. Finally, the binary union decoder is analyzed for three different fading conditions of the channel corresponding to conditions of atmospheric turbulence typical of weak, moderate, and superstrong scattering. Our findings show that the worst channel conditions for an optical communication system exist when the turbulence is moderate  相似文献   

8.
Zummo  S.A. 《Communications, IET》2008,2(4):538-544
New union bounds are derived for space-time block coded systems over Rayleigh fading channels. Both maximal ratio combining and generalised selection combining are considered as combining schemes at the receiver. The union bounds are easy to be evaluated using the transfer function of the code. Furthermore, the bounds are general to any coding scheme with a known weight distribution. Results show that the proposed union bounds are tight to simulation results for wide ranges of diversity orders and signal-to-noise ratio values.  相似文献   

9.
A particular kind of unit-distance code is proposed. Unit-distance codes are applied especially to absolute encoders (linear or rotary). The various positions of the encoder are represented by the various code words of the code. In contrast to conventional unit-distance codes, this code offers the possibility of detecting all single-bit errors except the two single-bit errors that cause a code word which represents the adjacent position. Unit-distance codes are characterized by a Hamming distance of 1. Thus, Hamming distance is not a unit of measurement for the code's error-detection ability. Therefore, a Hamming distance is defined especially for unit-distance codes excluding the adjacent code words from the calculation of distances. An application shows the utility of the code in the field of instrumentation and measurement  相似文献   

10.
In this paper the problem of calculating the probability of failure of linear dynamical systems subjected to random excitations is considered. The failure probability can be described as a union of failure events each of which is described by a linear limit state function. While the failure probability due to a union of non-interacting limit state functions can be evaluated without difficulty, the interaction among the limit state functions makes the calculation of the failure probability a difficult and challenging task. A novel robust reliability methodology, referred to as Wedge-Simulation-Method, is proposed to calculate the probability that the response of a linear system subjected to Gaussian random excitation exceeds specified target thresholds. A numerical example is given to demonstrate the efficiency of the proposed method which is found to be enormously more efficient than Monte Carlo Simulations.  相似文献   

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