利用有限仿射几何构作Cartesian认证码

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The Geometry of Elation Groups of a Finite Projective Space

We study the geometry of point-orbits of elation groups with a given center and axis of a finite projective space. We show that there exists a 1-1 correspondence from conjugacy classes of such groups and orbits on projective subspaces (of a suitable dimension) of Singer groups of projective spaces. Together with a recent result of Drudge [7] we establish the number of these elation groups.     

利用奇、偶特征的正交几何构作的最优Cartesian认证码

利用奇、偶特征有限域上的正交几何构作出一类C artesian认证码,并且计算了它们的参数.并在假定按照等概率分布来选择编码规则下,求出了认证码的成功的模仿攻击概率和成功的替换攻击概率.作为一个推论,还得到了一些最优的C artesian认证码.     

Long Binary Linear Codes and Large Caps in Projective Space

We obtain, in principle, a complete classification of all long inextendable binary linear codes. Several related constructions and results are presented.     

Weight Enumeration and the Geometry of Linear Codes

The problem of computing the weight distribution of a linear code is proved to be a special case of the problem of finding the Tutte polynomial (or generalized dichromatic polynomial) of a combinatorial geometry. Many other connections between the two fields are discussed.     

利用有限域上酉几何构作带仲裁的认证码

利用有限域上酉几何构作一类新的带仲裁的认证码,并且计算了所构作认证码的参数以及各种攻击成功的概率.     

利用有限域上奇异伪辛几何构作具有仲裁的认证码

A construction of authentication codes with arbitration from singular pseudo-symplectic geometry over finite fields is given and the parameters of the code are computed. Under the assumption that the encoding rules of the transmitter and the receiver are chosen according to a uniform probability distribution, the probabilities of success for different types of deceptions are also computed.     

利用有限域上奇异伪辛几何构作具有仲裁的认证码

利用有限域上奇异伪辛几何构作了一个新的具有仲裁的认证码,计算了这个码的参数,当发方编码规则和收方解码规则按等概率分布选取时,计算出各种攻击成功的概率.     

Linear Sections of the Finite Veronese Varieties and Authentication Systems Defined Using Geometry

In this paper we deal with authentication systems in which one key is used to authenticate many source states. We answer a related question on the cardinalities of the intersections of quadrics in PG (d,q). We first generalize a class of geometric authentication systems, which has been introduced by Beutelspacher, Tallini and Zanella4. The source states are the lines through a special point N of PG (d,q) (the d-dimensional projective space over GF (q)). The keys are some hypersurfaces which have N as a nucleus ( N is a nucleus of if every line through N meets in exactly one point). The message belonging to a source state and a key is the unique point of intersection of the line with the hypersurface . We give the values of s for which the constructed authentication systems have a security which is comparable to the best allowed by a theoretical bound. In case the hypersurfaces are quadrics, we give further results on the security. To this end, we determine the greatest cardinality for the intersections of the finite Veronese varieties with the projective subspaces of any given dimension. Finally, we discuss a possible implementation.     

透视画法的几何研究与计算机作图

对文艺复兴时写实绘画所采用的透视画法进行了精确的数学描述,并利用所得结论给出了使用计算机进行作图的方法.     

斜投影画法的几何研究与计算机作图

对中国古代写实绘画所采用的斜投影画法进行了精确的数学描述 ,并利用所得结论给出了使用计算机进行作图的方法 .     

Finite Projective Geometries and Classification of the Weight Hierarchies of Codes （Ⅰ）

The weight hierarchy of a binary linear [n,κ] code C is the sequence (d1,d2,...,dκ), where dr is the smallest support of an r-dimensional subcode of C. The codes of dimension 4 are collected in classes and the possible weight hierarchies in each class is determined by finite projective geometries.The possible weight hierarchies in class A, B, C, D are determined in Part (Ⅰ). The possible weight hierarchies in class E, F, G, H, I are determined in Part (Ⅱ).     

A Construction of Optimal Constant Composition Codes

In this paper, a construction of optimal constant composition codes is developed, and used to derive some series of new optimal constant composition codes meeting the upper bound given by [13].     

Classification of Some Optimal Ternary Linear Codes of Small Length

A classification is given of some optimal ternary linear codes of small length. Dimension 2 is classified for every minimum distance. Dimension 3, 4 and 5 is classified up to minimum distance 12. For higher dimension a classification is given where possible.     

利用有限域上的向量空间构作一种新的A~2-码

利用有限域上的向量空间的子空间作了一个A~2-码,并计算了该码的参数.在假定发方编码规则和收方解码规则按等概率分布选取时,计算了各种攻击成功的概率.     

USING FINITE UNITARY GEOMETRY TO CONSTRUCT A CLASS OF PBIB DESIGNS

In this paper the author considers the n-dimensional(n≥3)unitary geometry overfinite field F_(q~2),where q is a power of a prime,The author takesthe set of all one-dimensionalnon-isotropic subspaces as the set of treatments,and obtainsan association scheme and PBIBdesigns with q associate classes,whose parameters are also computed.     

Construction of MDS Self-dual Codes over Finite Fields

In this paper, we obtain some new results on the existence of MDS self-dual codes utilizing (extended) generalized Reed-Solomon codes over finite fields of odd characteristic. For finite field with odd characteristic and square cardinality, our results can produce more classes of MDS self-dual codes than previous works.     

Curves in Projective Spaces and Almost MDS Codes

A k-track in PG(n,q) is a set of k points such that every n of them are in general position. Here, we construct a class of n-tracks arising from algebraic curves.     

On Optimal Representatives of Finite Coloured Linear Orders

Order - Two structures A and B are n-equivalent if player II has a winning strategy in the n-move Ehrenfeucht-Fraïssé game on A and B. We extend earlier results about n-equivalence...