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.     

A rank-three condition for invariant (1, 2)-symplectic almost Hermitian structures on flag manifolds

This paper considers invariant (1, 2)-symplectic almost Hermitian structures on the maximal flag manifod associated to a complex semi-simple Lie group G. The concept of cone-free invariant almost complex structure is introduced. It involves the rank-three subgroups of G, and generalizes the cone-free property for tournaments related to 𝕊l (n,ℂ) case. It is proved that the cone-free property is necessary for an invariant almost-complex structure to take part in an invariant (1, 2)-symplectic almost Hermitian structure. It is also sufficient if the Lie group is not B _l , l ≥ 3, G ₂ or F ₄. For B _l and F ₄ a close condition turns out to be sufficient. Received: 28 October 2001     

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)     

Representing homology classes by locally flat 2-spheres

We prove an existence result for topologically locally flat embeddings of 2-spheres in simply connected 4-manifolds. This topological result is deduced from a splitting theorem for pointed Hermitian modules over a cyclic group ring. A stability result for such modules is also proved. This applies to the isotopy classification of locally flat embeddings.Partially supported by the NSF.     

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.      

量子Turbo码

量子纠错编码技术在量子通信和量子计算领域起着非常重要的作用.构造量子纠错编码的主要方法是借鉴经典纠错编码技术,目前几乎所有经典纠错编码方案都已经被移植到量子领域中来,然而在经典编码领域纠错性能最杰出的Turbo码却至今没有量子对应.提出了一种利用量子寄存器网络构造量子递归系统卷积码的简单实现方案,同时利用量子SWAP门设计了一种高效的量子交织器门组网络方案.最后仿照经典Turbo码的设计原理提出串行级联的量子Turbo码,同时提出了可行的译码方法.量子Turbo码不仅丰富了量子纠错码研究的领域,同时为解释 关键词： 量子递归系统卷积码 量子Turbo码 量子纠错编码 量子信息     

Veronese embedding and two–character sets

Two infinite families of two–character sets in PG(5,q) arising from the Veronese surface of PG(5,q) are constructed.     

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．