Binary construction of quantum codes of minimum distances five and six

In this paper, we construct a large number of good quantum codes of minimum distances five and six by Steane's Construction. Our methods involve the study of the check matrices of binary extended BCH-codes, together with puncturing and combining such matrices.     

量子稀疏图码的反馈式迭代译码

量子稀疏图码的译码可以由基于错误图样的和积译码算法来实现.本文在此基础上构建了一个新的反馈式迭代译码算法.其反馈策略不仅仅重新利用了错误图样,而且还利用了稳定子上相应元素的值和信道的错误模型.由此,本方法一方面可以克服传统的量子和积译码算法中遇到的所谓对称简并错误,另一方面还能反馈更多的有用信息到译码器中,帮助其产生有效的译码结果,大大提高译码器的译码能力.另外,本算法并没有增加量子测量的复杂度,而是对测量中所能获得的信息的更充分利用.     

混合长度为{4,5,6}的完备删位纠错码的存在性

依据刻画空间中向量间距离方式的不同,可定义不同的纠错码.Levenshtein定义了莱文斯坦距离,由此定义了删位纠错码.本文借助组合设计理论中的成对平衡设计以及初等数论的方法和技巧,给出参数为T{2,{4,5,6},v}的完备删位纠错码存在的两个必要条件,并确定了,当v≥4且v■{8,9,14}时,存在参数为T{2,{4,5,6},v}的完备删位纠错码.     

高压旋喷桩在基础纠偏中的应用

通过工程实例，讨论了在复杂地层、环境中高压旋喷桩技术的应用，为进一步扩大高压旋喷桩技术推广应用提供依据。     

移动数字信令中使用纠错码的检纠错性能分析

本文以一个典型移动数字信道为背景,利用已建立的三状态Markov模型参数求得在无交错和有交错两种不同情况下的信道错误分布概率P(n,m)和P_I(n,m);根据目前在移动数字信令中常用纠错码的对偶码的重量分布,利用了Macwilliams恒等式,计算出了这些码的重量分布A_i,最后由得到的A_i、P(n,m)和P_I(n,m)结果对有无交错两种不同情况下移动数字信令纠错码的检纠错能力进行了分析计算.     

L_1-norm packings from function fields

In this paper,we study some packings in a cube,namely,how to pack n points in a cube so as to maximize the minimal distance.The distance is induced by the L_1-norm which is analogous to the Hamming distance in coding theory.Two constructions with reasonable parameters are obtained,by using some results from a function field including divisor class group,narrow ray class group,and so on.We also present some asymptotic results of the two packings.     

环Z_p~m上循环码

揭示了环Zpm上码长为n的循环码的周期分布及其对偶码的周期分布的关系,给出了精确计算公式.     

生成量子稳定子码的种子生成器

为了解决生成量子稳定子码的码字时需先找出种子生成器的问题,将寻找种子生成器转化为解线性方程组及线性空间中向量组线性相关和线性无关问题,提出了快速判决法、排序查找法和求解方程组方法来验证找到的算子是否为合法的种子生成器.将稳定子与种子生成器同时标准化可以快速得到量子稳定子码的编码电路.给出了稳定子码种子生成器总数和编码电路所需要的2-qubit和1-qubit门数量.该方法既能用于同时包含Ⅰ型和Ⅱ型生成元的量子稳定子码,又能用于仅含Ⅰ型生成元的量子稳定子码,得到的种子生成器仅含X算子,故编码电路简单.     

Universal Framework for Quantum Error-Correcting Codes

We present a universal framework for quantum error-correcting codes, i.e., a framework that applies to the most general quantum error-correcting codes. This framework is based on the group algebra, an algebraic notation associated with nice error bases of quantum systems. The nicest thing about this framework is that we can characterize the properties of quantum codes by the properties of the group algebra. We show how it characterizes the properties of quantum codes as well as generates some new results about quantum codes.     

Error-Correcting Codes over an Alphabet of Four Elements

The problem of finding the values of A_q(n,d)—the maximum size of a code of length n and minimum distance d over an alphabet of q elements—is considered. Upper and lower bounds on A₄(n,d) are presented and some values of this function are settled. A table of best known bounds on A₄(n,d) is given for n 12. When q M < 2q, all parameters for which A_q(n,d) = M are determined.