Veronese Varieties Over Finite Fields and Their Projections

Inthis paper Veronese varieties of degree d over aGalois field are studied. We also show that some of known capsembedded into classical varieties always are projections of Veronesevarieties.     

利用有限仿射几何构作Cartesian认证码

设 0 相似文献   

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

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.     

利用辛几何构作两类Cartesian认证码

本文利用辛几何构作了两类 Cartesian认证码 ,计算了码的参数 .当编码规则按等概率分布选取时 ,计算出敌方成功的模仿攻击概率和成功的替换攻击概率     

利用有限域上一类幂零阵的标准形构造Cartesian认证码

Let Fq be a finite field. In this paper, a construction of Cartesian au-thentication codes from the normal form of a class of nilpotent matrices over the field Fq is presented. Moreover, assume that the encoding rules are chosen according to a uniform probability distribution, the probabilities PI and PS, of a successful im-personation attack and of a successful substitution attack respectively, of these codes are also computed.     

利用有限域上特征为2的正交几何构作一类Cartesian认证码

利用了有限域上的特征为2的正交几何构造了一类Cartesian认证码,并且计算了其参数及模仿攻击成功的概率PI和替换攻击成功的概率PS.     

Using Normal Form of Idempotent Matrices over Finite Local Ring Z/p^kZ to Construct Cartesian Authentication Codes

In this paper, we determine the normal forms of idempotent matrices for similarity over finite local rings Z/p^kZ, from which we construct a Cartesian authentication code and compute its size parameters and the probabilities of successful impersonation and substitution attack under the hypothesis that the cecoding rules are chosen according to a uniform probability distribution.     

利用有限局部环Z/pkZ上的幂等矩阵的标准型构作认证码

In this paper,we determine the normal forms of idempotent matrices for similarity over finite local rings Z/p~kZ,from which we construct a Cartesian au- thentication code and compute its size parameters and the probabilities of successful impersonation and substitution attack under the hypothesis that the cecoding rules are chosen according to a uniform probability distribution.     

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.     

Geometry of Cubic and Quartic Hypersurfaces over Finite Fields

Let YPⁿ be a cubic hypersurface defined over GF(q). Here, we study the Finite Field Nullstellensatz of order [q/3] for the set Y(q) of its GF(q)-points, the existence of linear subspaces of PG(n,q) contained in Y(q) and the possibility to join any two points of Y(q) by the union of two lines of PG(n,q) entirely contained in Y(q). We also study the existence of linear subspaces defined over GF(q) for the intersection of Y with s quadrics and for quartic hypersurfaces.     

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.     

Hyperplane Sections of Grassmannians and the Number of MDS Linear Codes

We obtain some effective lower and upper bounds for the number of (n,k)-MDS linear codes over _q. As a consequence, one obtains an asymptotic formula for this number. These results also apply for the number of inequivalent representations over _q of the uniform matroid or, alternately, the number of _q-rational points of certain open strata of Grassmannians. The techniques used in the determination of bounds for the number of MDS codes are applied to deduce several geometric properties of certain sections of Grassmannians by coordinate hyperplanes.     

An Arithmetic Reduction of Finite Rank 3 Geometries with Linear Spaces as Plane Residues and with Dual Linear Spaces as Point Residues

Let be a rank three incidence geometry of points, lines and planes whose planes are linear spaces and whose point residues are dual linear spaces (notice that we do not require anything on the line residues). We assume that the residual linear spaces of belong to a natural class of finite linear spaces, namely those linear spaces whose full automorphism group acts flag-transitively and whose orders are polynomial functions of some prime number. This class consists of six families of linear spaces. In the amalgamation of two such linear spaces imposes an equality on their orders leading, in particular, to a series of diophantine equations, the solutions of which provide a reduction theorem on the possible amalgams of linear spaces that can occur in .We prove that one of the following holds (up to a permutation of the words point and plane):A) the planes of and the dual of the point residues belong to the same family and have the same orders,B) the diagram of is in one of six families,C) the diagram of belongs to a list of seven sporadic cases.Finally, we consider the particular case where the line residues of are generalized digons.     

A Combinatorial Algorithm Related to the Geometry of the Moduli Space of Pointed Curves

As pointed out in Arbarello and Cornalba (J. Alg. Geom. 5 (1996), 705–749), a theorem due to Di Francesco, Itzykson, and Zuber (see Di Francesco, Itzykson, and Zuber, Commun. Math. Phys. 151 (1993), 193–219) should yield new relations among cohomology classes of the moduli space of pointed curves. The coefficients appearing in these new relations can be determined by the algorithm we introduce in this paper.     

On the Minimum Length of some Linear Codes of Dimension 5

In this paper, we shall prove that the minimum length n_q(5,d) is equal to g_q(5,d) +1 for q⁴−2q²−2q+1≤ d≤ q⁴ − 2q² − q and 2q⁴ − 2q³ − q² − 2q+1 ≤ d ≤ 2q⁴−2q³−q²−q, where g_q(5,d) means the Griesmer bound . Communicated by: J.D. Key     

Order Varieties and Monotone Retractions of Finite Posets

In this paper we introduce a new version of the concept of order varieties. Namely, in addition to closure under retracts and products we require that the class of posets should be closed under taking idempotent subalgebras. As an application we prove that the variety generated by an order-primal algebra on a finite connected poset P is congruence modular if and only if every idempotent subalgebra of P is connected. We give a polynomial time algorithm to decide whether or not a variety generated by an order-primal algebra admits a near unanimity function and so we answer a problem of Larose and Zádori.     

Characterization of the Existence of an Enriched Linear Finite Element Approximation Using Biorthogonal Systems

The present paper is intended to give a characterization of the existence of an enriched linear finite element approximation based on biorthogonal systems. It is shown that the enriched element exists if and only if a certain multivariate generalized trapezoidal type cubature formula has a nonzero approximation error. Furthermore, for such an enriched element we derive simple explicit formulas for the basis functions, and show that the approximation error can be written as the sum of the error of the (non-enriched) element plus a perturbation that depends on the enrichment function. Finally, we estimate the approximation error in L² norm. We also give an alternative approach to estimate the approximation error, which relies on an appropriate use of the Poincaré inequality.     

A Characterization of Some Minihypers and its Application to Linear Codes

Any {f,r- 2+s; r,q}-minihyper includes a hyperplane in PG(r, q) if fr-1 + s 1 + q – 1 for 1 s q – 1, q 3, r 4, where i = (qi + 1 – 1)/ (q – 1 ). A lower bound on f for which an {f, r – 2 + 1; r, q}-minihyper with q 3, r 4 exists is also given. As an application to coding theory, we show the nonexistence of [ n, k, n + 1 – qk – 2 ]q codes for k 5, q 3 for qk – 1 – 2q – 1 < n qk – 1 – q – 1 when k > q – q - \sqrt q + 2$$ " align="middle" border="0"> and for when , which is a generalization of [18, Them. 2.4].