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.     

Higher Grassmann codes

We compute the parameters of the linear codes that are associated with all projective embeddings of Grassmann varieties.     

Fortran codes for the correlation functions of hard sphere fluids

Our Fortran codes for hard sphere fluids and their mixtures for the correlation functions that arise from the Percus–Yevick theory and the Verlet–Weis semi-empirical correction have proven useful during a period of nearly four decades and continue to be useful. In order to make these codes even more widely available, a brief summary is presented here and listings of these codes are given in the electronically accessible Supplementary Material to this paper.     

Spin glasses and information

After a brief introduction to information theory, we review the close relationship between the theory of spin glasses and information processing, error-correcting codes in particular. An interesting equivalence of the solvability condition of the spin glass problem and the optimal inference condition in information theory is pointed out.     

具有优良渐近参数的代数几何码

本文讨论了一类具有好的渐近参数的代数几何码.通过对除子类数、高次有理除子数以及代数几何码的参数分析,得到一类码其渐近界优于Gilbert-Varshamov界和Xing界.在这两个界的交点处,渐近界有所改进.     

The Double Self-Dual Gravity with Cosmological Term and Constraints Under the Double Constant Conformal Transformation

The double constraint equations in the self-dual gravitational theory containing the cosmological term are derived in 3 + 1 gravity. Furthermore, in order to deeply study the Lorentzian and Euclidean reality conditions for this theory, the relations between constraints are discussed by introducing the double constant conformal transformation and the double complex function method.     

Codes from Generalized Hexagons

In this paper, we construct some codes that arise from generalized hexagons with small parameters. As our main result we discover two new projective two-weight codes constructed from two-character sets in PG(5,4) and PG(11,2). These in turn are constructed using a new distance-2-ovoid of the classical generalized hexagon H(4). Also the corresponding strongly regular graph is new. The two-character set is the union of two orbits in PG(5,4) under the action of L₂(13). Communicated by: R. Calderbank The first Author is Research Assistant of the Fund for Scientific Research - Flanders (Belgium) (F.W.O)     

Extremal self-dual codes of length 64 through neighbors and covering radii

We construct extremal singly even self-dual [64,32,12] codes with weight enumerators which were not known to be attainable. In particular, we find some codes whose shadows have minimum weight 12. By considering their doubly even neighbors, extremal doubly even self-dual [64,32,12] codes with covering radius 12 are constructed for the first time.     

Sliding-window dynamic frameproof codes

A sliding-window dynamic frameproof code is a scheme for discouraging the piracy of digital broadcasts through the use of digital fingerprinting. In this paper, we formally define sliding-window dynamic frameproof codes and provide optimal constructions for a certain class of these schemes. We also discuss bounds on the number of users such schemes can support.