共查询到20条相似文献,搜索用时 31 毫秒
1.
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
2.
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
3.
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
4.
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
5.
We introduce the notion of hyper-self-duality for Bose-Mesner algebras as a strengthening of formal self-duality. Let
denote a Bose-Mesner algebra on a finite nonempty set X. Fix p X, and let
and
denote respectively the dual Bose-Mesner algebra and the Terwilliger algebra of
with respect to p. By a hyper-duality of
, we mean an automorphism of
such that
for all
; and
is a duality of
.
is said to be hyper-self-dual whenever there exists a hyper-duality of
. We say that
is strongly hyper-self-dual whenever there exists a hyper-duality of
which can be expressed as conjugation by an invertible element of
. We show that Bose-Mesner algebras which support a spin model are strongly hyper-self-dual, and we characterize strong hyper-self-duality via the module structure of the associated Terwilliger algebra. 相似文献
6.
We consider the extremal problem to determine the maximal number
of columns of a 0-1 matrix with
rows and at most
ones in each column such that each
columns are linearly independent modulo
. For fixed integers
and
, we shall prove the probabilistic lower bound
=
; for
a power of
, we prove the upper bound
which matches the lower bound for infinitely many values of
. We give some explicit constructions. 相似文献
7.
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
8.
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
9.
A. J. van Zanten 《Designs, Codes and Cryptography》1997,10(1):85-97
Let
be a list of all words of
, lexicographically ordered with respect to some basis. Lexicodes are codes constructed from
by applying a greedy algorithm. A short proof, only based on simple principles from linear algebra, is given for the linearity of these codes. The proof holds for any ordered basis, and for any selection criterion, thus generalizing the results of several authors. An extension of the applied technique shows that lexicodes over
are linear for a wide choice of bases and for a large class of selection criteria. This result generalizes a property of Conway and Sloane. 相似文献
10.
Let
be an
-filtered category in the sense of Karoubi. This is the categorical analogue of an ideal
in a ring
. Pedersen and Weibel constructed a fibration of K-theory spectra associated with the sequence
. We present a new easier proof based on Waldhausen' generic fibration. 相似文献
11.
Natalie M. Priebe 《Geometriae Dedicata》2000,79(3):239-265
In this paper, a technique for analyzing levels of hierarchy in a tiling
of Euclidean space is presented. Fixing a central configuration P of tiles in
, a `derived Voronoï' tessellation
P is constructed based on the locations of copies of P in
. A family of derived Voronoï tilings
is formed by allowing the central configurations to vary through an infinite number of possibilities. The family
will normally be an infinite one, but we show that for a self-similar tiling
it is finite up to similarity. In addition, we show that if the family
is finite up to similarity, then
is pseudo-self-similar. The relationship between self-similarity and pseudo-self-similarity is not well understood, and this is the obstruction to a complete characterization of self-similarity via our method. A discussion and conjecture on the connection between the two forms of hierarchy for tilings is provided. 相似文献
12.
O. V. Sarafanov 《Journal of Mathematical Sciences》2004,120(2):1195-1239
The C
*-algebra
generated by the operators of pseudodifferential boundary value problems on a manifold
with smooth closed disjoint edges and boundary
is studied. The operators act in the space L
2(
)
L
2(
). The goal of this paper is to describe all (up to an equivalence) irreducible representations of the algebra
Bibliography: 12 titles. 相似文献
13.
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
14.
Niels Jakob Laustsen 《K-Theory》2001,23(2):115-127
We prove that the K-groups of the Banach algebra
of bounded, linear operators on the pth James space
, where 1 < p < , are given by
and
. Moreover, for each Banach space
and each non-zero, closed ideal
contained in the ideal of inessential operators, we show that
and
. This enables us to calculate the K-groups of
for each Banach space
which is a direct sum of finitely many James spaces and
-spaces. 相似文献
15.
Izu Vaisman 《Annals of Global Analysis and Geometry》2001,19(3):209-234
The transversal twistor space of a foliation
of an even codimension is the bundle
of the complex structures of the fibers of the transversalbundle of
. On
there exists a foliation
by covering spaces of the leaves of
, and any Bottconnection of
produces an ordered pair
of transversal almost complex structures of
. The existence of a Bott connection which yields a structure
1 that is projectable to the space of leaves isequivalent to the fact that
is a transversallyprojective foliation. A Bott connection which yields a projectablestructure
2 exists iff
isa transversally projective foliation which satisfies a supplementarycohomological condition, and, in this case,
1is projectable as well.
2 is never integrable.The essential integrability condition of
1 isthe flatness of the transversal projective structure of
. 相似文献
16.
Vladimir I. Levenshtein 《Designs, Codes and Cryptography》1997,12(2):131-160
A system of (Boolean) functions in
variables is called randomized if the functions preserve the property of their variables to be independent and uniformly distributed random variables. Such a system is referred to as
-resilient if for any substitution of constants for any
variables, where 0 i t, the derived system of functions in
variables will be also randomized. We investigate the problem of finding the maximum number
of functions in
variables of which any
form a
-resilient system. This problem is reduced to the minimization of the size of certain combinatorial designs, which we call split orthogonal arrays. We extend some results of design and coding theory, in particular, a duality in bounding the optimal sizes of codes and designs, in order to obtain upper and lower bounds on
. In some cases, these bounds turn out to be very tight. In particular, for some infinite subsequences of integers
they allow us to prove that
,
,
,
,
. We also find a connection of the problem considered with the construction of unequal-error-protection codes and superimposed codes for multiple access in the Hamming channel. 相似文献
17.
In this paper, we consider equations of the form
, where
is a function with values in the Hilbert space
, the operator B is symmetric, and the operator A is uniformly positive and self-adjoint in
. The linear operator
generating the C
0-semigroup in the energy space
is associated with this equation. We prove that this semigroup is exponentially stable if the operator B is uniformly positive and the operator A dominates B in the sense of quadratic forms. 相似文献
18.
Let
be a hereditary torsion theory for the category
-mod of unital left
-modules over an associative ring
with an identity element. The purpose of this note is to prove that if the associated Gabriel filter
consists of finitely presented left ideals, then every module has a
-injective cover and if
contains a cofinal subset of finitely presented left ideals, then every module has a
-torsionfree
-injective cover. The methods used working with pure submodules contained in ``large" submodules also allow to unify the proofs of some previously known results. 相似文献
19.
We show that the automorphism group of a divisible design
is isomorphic to a subgroup H of index 1 or 2 in the automorphism group
of the associated constant weight code. Only in very special cases H is not the full automorphism group. 相似文献
20.
Ján Jakubík 《Czechoslovak Mathematical Journal》2002,52(3):651-663
Let Int
be the lattice of all intervals of an MV-algebra
. In the present paper we investigate the relations between direct product decompositions of
and (i) the lattice Int
, or (ii) 2-periodic isometries on
, respectively. 相似文献