利用伪辛空间中2维全迷向子空间构作结合方案与PBIB设计

取有限域Ｆｑ上２×２＋２维伪辛空间中２维全迷向子空间作为处理，构作了具有４个结合类和２个结合类的结合方案与ＰＢＩＢ设计，并且计算了它们的参数     

利用有限仿射空间中直线构作结合方案与PBIB设计

利用有限仿射空间ＡＧ（ｎ，Ｆｑ）中的直线作为处理，在ｎ＝２和ｎ≥３时分别构作了类数为２和３的结合方案，计算了其参数，并且利用所得到的结合方案构作了若干个ＰＢＩＢ设计。     

利用有限几何构作3-PBIB（2）设计和3-设计

The concept of t-PBIB design was introduced by Wei Wandi and Yang Benfu as a generalization of G-design and PBIB design. In this paper, a number of 3-associntion schemes and 3-PBIB(2) designs are constructed on the bases of the finite vector space over Fq and the finite unitary geometry over Fq2. Then a number of 3-designs are constructed on the bases of the finite orthogonal geometries over Fq. The parameters of all these designs are computed.     

一类容错码的构作和它的汉明距离

利用有限域上辛空间的极大全迷向子空间及其入一元组构作了一类容错码,并利用辛空间上的计数公式给出了这类容错码的汉明距离.     

特征为2的有限域上伪辛群作用在m维全迷向子空间集上的次轨道

本文讨论特征为２的有限域上伪辛几何中，在伪辛群Ｐ＿（ｓ２ｖ＋δ）（Ｆ＿ｑ）作用下ｍ维全迷向子空间可迁集的次轨道．并计算出非平凡轨道的个数及次轨道的长．     

有限几何和PBIB设计(Ⅱ)

在有限辛几何中,取定一个(m,s)型子空间,并取与这个子空间正交且不含于这个子空间的一维子空间作处理,我们构作了一些结合方案和PBIB设计,并计算了它们的参数.     

利用特征为2有限域上伪辛几何中（2,1）型子空间构作PBIB设计

§1.引言 关于结合方案和PBIB设计的定义及所用的有关符号见文献[1].有关的工作见[2-4]。 设F_q为特征2的有限域.我们将用F_q上的对称阵     

利用有限域上向量空间的子空间构作PBIB设计

设q是一个素数幂,F_q是有q个元素的有限域,V_n(F_q)表示F_q上的n维向量空间。在文献[1],[2]中,利用V_n(F_q)中m维子空间作处理构作了一个具有min{m,n-m}个结合类的结合方案和一些PBIB设计。本文先给出一般线性群GL_n(F_q)的一个新的可迁性定理和有关子空间的一个新的计数定理,然后构作了一类广泛的新设计,以[2]中第6章的定理8、9、10为其特例。     

PBIB设计的约化

设Ｄ是一个有ｍ个结合类的ＰＢＩＢ设计，且它的参数λ１，λ２，．．．，λｍ中至少有两个是相等，第二节中，给出了ＰＢＩＢ设计Ｄ可以用遂次合并结合类来约化的充分必要条件，第三节给出了ＰＢＩＢ设计Ｄ可以用同时合并结合来约化的充分必要条件，最后，在第四节里我们研究了上述两种方法之间的关系。     

一族4－PBIB设计

一族４－ＰＢＩＢ设计陈瑞琛（杨州大学师范学院数学系，２２５００２）关键词ｔ－ＰＢＩＢ设计，有限域，反演平面．分类号ＡＭＳ（１９９１）０５Ｂ０５，５１Ｅ０５／ＣＣＬＯ１５７．２最近魏万迪和阳本傅￣［１］引进ｔ－ＰＢＩＢ设计概念，研究了它们的性质，并作出...     

Constructions of Group Divisible Designs

In this paper we present constructions for group divisible designs from generalized partial difference matrices. We describe some classes of examples.     

Kirkman Packing Designs KPD ({3, 5*},v)

A Kirkman packing design KPD ({3, 5^*},v) is a resolvable packing with maximum possible number of parallel classes, each class containing one block of size 5 and all other blocks of size three. Such designs can be used to construct certain threshold schemes in cryptography. In this paper, direct and recursive constructions are discussed for such designs. The existence of a KPD ({3, 5^*},v) for is established with a few possible exceptions.     

Some Observations on Quasi-3 Designs and Hadamard Matrices

We consider Hadamard matrices with the quasi-3 property, and their implications for the existence of certain quasi-symmetric designs. We find necessary conditions on the parameters, and show that the quasi-3 property is preserved by the Kronecker product.     

Association schemes based on maximal totally isotropic subspaces in singular pseudo-symplectic spaces

This paper provides some new families of symmetric association schemes based on maximal totally isotropic subspaces in (singular) pseudo-symplectic spaces. All intersection numbers of these schemes are computed.     

General Constructions for Double Group Divisible Designs and Double Frames

We generalize the concept of an incomplete double group divisible design and describe some recursive constructions for such a generalized new design. As a consequence, we obtain a general recursive construction for group divisible designs, which unifies many important recursive constructions for various types of combinatorial designs. We also introduce the concept of a double frame. After providing a preliminary result on the number of partial resolution classes, we describe a general construction for double frames. This construction method can unify many known recursive constructions for frames.     

Intersection Numbers For Subspace Designs

Intersection numbers for subspace designs are introduced and q‐analogs of the Mendelsohn and Köhler equations are given. As an application, we are able to determine the intersection structure of a putative q‐analog of the Fano plane for any prime power q. It is shown that its existence implies the existence of a 2‐ subspace design. Furthermore, several simplified or alternative proofs concerning intersection numbers of ordinary block designs are discussed.     

Constructions and Bounds for Unconditionally Secure Non-Interactive Commitment Schemes

Commitment schemes have been extensively studied since they were introduced by Blum in 1982. Rivest recently showed how to construct unconditionally secure non-interactive commitment schemes, assuming the existence of a trusted initializer. In this paper, we present a formal mathematical model for unconditionally secure non-interactive commitment schemes with a trusted initializer and analyze their binding and concealing properties. In particular, we show that such schemes cannot be perfectly binding: there is necessarily a small probability that Alice can cheat Bob by committing to one value but later revealing a different value. We prove several bounds on Alice's cheating probability, and present constructions of schemes that achieve optimal cheating probabilities. We also analyze a class of commitment schemes based on resolvable designs.     

USING FINITE GEOMETRIES TO CONSTRUCT 3-PBIB(2) DESIGNS AND 3-DESIGNS

ＵＳＩＮＧＦＩＮＩＴＥＧＥＯＭＥＴＲＩＥＳＴＯＣＯＮＳＴＲＵＣＴ３－ＰＢＩＢ（２）ＤＥＳＩＧＮＳＡＮＤ３－ＤＥＳＩＧＮＳ￥ＹＡＮＧＢＥＮＦＵ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＣｈｅｎｇｄｕＴｅａｃｈｅｒｓＣｏｌｌｅｇｅ，Ｃｈｅｎｇｄｕ...     

Constructions of 1 1/2-designs from symplectic geometry over finite fields

In this paper, we construct some 1(1/2)-designs, which are also known as partial geometric designs, using totally isotropic subspaces of the symplectic space and generalized symplectic graphs. Furthermore, these 1(1/2)-designs yield six infinite families of directed strongly regular graphs.