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1.
There are exactlytwo non-equivalent [32,11,12]-codes in the binaryReed-Muller code
which contain
and have the weight set {0,12,16,20,32}. Alternatively,the 4-spaces in the projective space
over the vector space
for which all points have rank 4 fall into exactlytwo orbits under the natural action of PGL(5) on
. 相似文献
2.
Massimo Giulietti Fernanda Pambianco Fernando Torres Emanuela Ughi 《Designs, Codes and Cryptography》2002,25(3):237-246
We point out an interplay between
-Frobenius non-classical plane curves and complete
-arcs in
. A typical example that shows how this works is the one concerning an Hermitian curve. We present some other examples here which give rise to the existence of new complete
-arcs with parameters
and
being a power of the characteristic. In addition, for q a square, new complete
-arcs with either
and
or
and
are constructed by using certain reducible plane curves. 相似文献
3.
B. N. Cooperstein 《Designs, Codes and Cryptography》2001,23(2):185-196
The projective plane
is embedded as a variety of projective points
in
, where M is a nine dimensional
-module for the groupG=GL(3,q
2). The hyperplane sections of thisvariety and their stabilizers in the group G aredetermined. When q 2 (mod 3) one such hyperplanesection is a member of the family of Kantor's unitary ovoids.We furtherdetermine all sections
whereD has codimension two in M and demonstratethat these are never empty. Consequences are drawn for Kantor'sovoids. 相似文献
4.
Let
be a unital C*-algebra and G the group of units of
. A geometrical study of the action of G over the set
+ of all positive elements of
is presented. The orbits of elements with closed range by this action are provided with a structure of differentiable homogeneous space with a natural connection. The orbits are partitioned in 'components' which also have a rich geometrical structure. 相似文献
5.
The automorphism group of the Barnes-Wall lattice L
m in dimension 2
m
(m ; 3) is a subgroup of index 2 in a certain Clifford group
of structure 2
+
1+2m
. O
+(2m,2). This group and its complex analogue
of structure
.Sp(2m, 2) have arisen in recent years in connection with the construction of orthogonal spreads, Kerdock sets, packings in Grassmannian spaces, quantum codes, Siegel modular forms and spherical designs. In this paper we give a simpler proof of Runge@apos;s 1996 result that the space of invariants for
of degree 2k is spanned by the complete weight enumerators of the codes
, where C ranges over all binary self-dual codes of length 2k; these are a basis if m k - 1. We also give new constructions for L
m and
: let M be the
-lattice with Gram matrix
. Then L
m is the rational part of M
m, and
= Aut(Mm). Also, if C is a binary self-dual code not generated by vectors of weight 2, then
is precisely the automorphism group of the complete weight enumerator of
. There are analogues of all these results for the complex group
, with doubly-even self-dual code instead of self-dual code. 相似文献
6.
J. A. Thas 《Designs, Codes and Cryptography》2001,23(2):249-258
If x is a regular point of the generalizedquadrangle
of order (s,t), s 1 t, then x defines a dual net
. If
contains a line L of regularpoints and if for at least one point x on Lthe automorphism group of the dual net
satisfies certain transitivityproperties, then
is a translation generalized quadrangle. Thisresult has many applications. We give one example. Ifs=t 1, then
is a dual affine plane. Let
be a generalizedquadrangle of orders,s odd and s 1, which contains a lineL of regular points. If for at least one pointx on L the plane
is Desarguesian, then
is isomorphic to the classical generalizedquadrangleW(s). 相似文献
7.
A (4,9)-set of size 829 in
(2,53) is constructed, as is a (4,11)-set of size 3189 in
(2,73). 相似文献
8.
A. I. Budkin 《Algebra and Logic》2000,39(6):363-369
Let
be a class of all groups G for which the normal closure (x)
G
of every element x belongs to a class
.
is a Levi class generated by
. Let
and
0 be classes of finitely generated nilpotent groups and of torsion-free, finitely generated, nilpotent groups, respectively. We prove that
and
, and so
and
. It is shown that quasivarieties
and
are closed under free products, and that each contains at most one maximal proper subquasivariety. It is also proved that
is closed under free products if so is
. 相似文献
9.
An extension of the auxiliary problem principle to variational inequalities with non-symmetric multi-valued operators in Hilbert spaces is studied. This extension concerns the case that the operator is split into the sum of a single-valued operator
, possessing a kind of pseudo Dunn property, and a maximal monotone operator
. The current auxiliary problem is k constructed by fixing
at the previous iterate, whereas
(or its single-valued approximation
k) k is considered at a variable point. Using auxiliary operators of the form
k+
, with k>0, the standard for the auxiliary problem principle assumption of the strong convexity of the function h can be weakened exploiting mutual properties of
and h. Convergence of the general scheme is analyzed and some applications are sketched briefly. 相似文献
10.
Let
= {a
1, a
2,...} be a set of positive integers and let p
(n) and q
(n) denote the number of partitions of n into a's, resp. distinct a's. In an earlier paper the authors studied large values of log(max (2,p
(n)))/log(max(2,q
(n))). In this paper the small values of the same quotient are studied. 相似文献
11.
This article improves results of Hamada, Helleseth and Maekawa on minihypers in projective spaces and linear codes meeting the Griesmer bound.In [10,12],it was shown that any
-minihyper, with
, where
, is the disjoint union of
points,
lines,...,
-dimensional subspaces. For q large, we improve on this result by increasing the upper bound on
non-square, to
non-square,
square,
, and (4) for
square, p prime, p<3, to
. In the case q non-square, the conclusion is the same as written above; the minihyper is the disjoint union of subspaces. When q is square however, the minihyper is either the disjoint union of subspaces, or the disjoint union of subspaces and one subgeometry
. For the coding-theoretical problem, our results classify the corresponding
codes meeting the Griesmer bound. 相似文献
12.
Koen Thas 《Designs, Codes and Cryptography》2002,25(3):247-253
Suppose
is a generalized quadrangle (GQ) of order
, with a regular point. Then there is a net which arises from this regular point. We prove that if such a net has a proper subnet with the same degree as the net, then it must be an affine plane of order t. Also, this affine plane induces a proper subquadrangle of order t containing the regular point, and we necessarily have that
. This result has many applications, of which we give one example. Suppose
is an elation generalized quadrangle (EGQ) of order
, with elation point p. Then
is called a skew translation generalized quadrangle (STGQ) with base-point p if there is a full group of symmetries about p of order t which is contained in the elation group. We show that a GQ
of order s is an STGQ with base-point p if and only if p is an elation point which is regular. 相似文献
13.
For a discrete group G, we prove that a G-map between proper G–CW-complexes induces an isomorphism in G-equivariant K-homology if it induces an isomorphism in C-equivariant K-homology for every finite cyclic subgroup C of G. As an application, we show that the source of the Baum–Connes assembly map, namely K
*
G
(E(G,
in)), is isomorphic to K
*
G
(E(G,
)), where E(G,
) denotes the classifying space for the family of finite cyclic subgroups of G. Letting
be the family of virtually cyclic subgroups of G, we also establish that and related results. 相似文献
14.
The concepts of an annihilator and a relative annihilator in an autometrized l-algebra are introduced. It is shown that every relative annihilator in a normal autometrized l-algebra
is an ideal of
and every principal ideal of
is an annihilator of
. The set of all annihilators of
forms a complete lattice. The concept of an I-polar is introduced for every ideal I of
. The set of all I-polars is a complete lattice which becomes a two-element chain provided I is prime. The I-polars are characterized as pseudocomplements in the lattice of all ideals of
containing I. 相似文献
15.
A. I. Budkin 《Algebra and Logic》2005,44(4):213-218
Let qG be a quasivariety generated by a group G and
be a non-Abelian quasivariety of groups with a finite lattice of subquasivarieties. Suppose
is contained in a quasivariety generated by the following two groups: a free 2-nilpotent group F2(
2) of rank 2 and a free metabelian (i.e., with an Abelian commutant) group F2(
2) of rank 2. It is proved that either
= qF2(
2) or
= qF2(
2) in this instance.__________Translated from Algebra i Logika, Vol. 44, No. 4, pp. 389–398, July–August, 2005. 相似文献
16.
U. Dempwolff 《Designs, Codes and Cryptography》2001,22(2):191-207
We determine the symmetric designs
which admit a group
such that G has a nonabelian socle and is a primitiverank 3 group on points (and blocks). 相似文献
17.
František Machala 《Czechoslovak Mathematical Journal》2003,53(1):9-18
Every incidence structure
(understood as a triple of sets (G, M, I), I G×M) admits for every positive integer p an incidence structure
where G
p (M
p) consists of all independent p-element subsets in G (M) and I
p
is determined by some bijections. In the paper such incidence structures
are investigated the
's of which have their incidence graphs of the simple join form. Some concrete illustrations are included with small sets G and M. 相似文献
18.
Aderemi Kuku 《K-Theory》2001,22(4):367-392
Let
be a rational prime,
an exact category. In this article, we define and study for all
, the profinite higher K-theory of
, that is
as well as
, where
is the
-dimensional mod-
Moore space. We study connections between
and prove several
-completeness results involving these and associated groups including the cases where
is the category of finitely generated (resp. finitely generated projective) modules over orders in semi-simple algebras over number fields and p-adic fields. We also define and study continuous K-theory
of orders in p-adic semi-simple algebras and show some connection between the profinite and continuous K-theory of . 相似文献
19.
Yutaka Hiramine 《Geometriae Dedicata》1993,48(2):139-189
In this paper we consider finite nets of orderq
2 and degreeq + 1 which admit GL(2,q). Our main result says that if a net
of orderq
2 and degreeq + 1 admits a collineation group with a point-regular normal subgroupT such that /T GL(2,q), then
is isomorphic to a regulus net, a twisted regulus net, a Hering net, or
. Except in the last one, each of them corresponds to a surface in PG(3,q) obtained from a homogeneous polynomial in two variables. 相似文献
20.
Ron M. Roth 《Designs, Codes and Cryptography》1996,9(2):177-191
Codes
of length 2
m
over {1, -1} are defined as null spaces of certain submatrices of Hadamard matrices. It is shown that the codewords of
all have an rth order spectral null at zero frequency. Establishing the connection between
and the parity-check matrix of Reed-Muller codes, the minimum distance of
is obtained along with upper bounds on the redundancy of
. An efficient algorithm is presented for encoding unconstrained binary sequences into
. 相似文献