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1.
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
2.
Tatsuya Maruta 《Designs, Codes and Cryptography》2001,22(2):165-177
There do not exist
codes over the Galois field GF
attaining the Griesmer bound for
for
andfor
for
. 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.
We reinterpret the state space dimension equations for geometric Goppa codes. An easy consequence is that if deg
then the state complexity of
is equal to the Wolf bound. For deg
, we use Clifford's theorem to give a simple lower bound on the state complexity of
. We then derive two further lower bounds on the state space dimensions of
in terms of the gonality sequence of
. (The gonality sequence is known for many of the function fields of interest for defining geometric Goppa codes.) One of the gonality bounds uses previous results on the generalised weight hierarchy of
and one follows in a straightforward way from first principles; often they are equal. For Hermitian codes both gonality bounds are equal to the DLP lower bound on state space dimensions. We conclude by using these results to calculate the DLP lower bound on state complexity for Hermitian codes. 相似文献
5.
Koichi Betsumiya T. Aaron Gulliver Masaaki Harada 《Designs, Codes and Cryptography》2003,28(2):171-186
In this paper, it is shown that extremal (Hermitian) self-dual codes over
2 ×
2 exist only for lengths 1, 2, 3, 4, 5, 8 and 10. All extremal self-dual codes over
2 ×
2 are found. In particular, it is shown that there is a unique extremal self-dual code up to equivalence for lengths 8 and 10. Optimal self-dual codes are also investigated. A classification is given for binary [12, 7, 4] codes with dual distance 4, binary [13, 7, 4] codes with dual distance 4 and binary [13, 8, 4] codes with dual distance 4. 相似文献
6.
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
7.
Judita Lihová 《Czechoslovak Mathematical Journal》1999,49(1):67-80
Let
be a partially ordered set, Int
the system of all (nonempty) intervals of
partially ordered by the set-theoretical inclusion
. We are interested in partially ordered sets
with Int
isomorphic to Int
. We are going to show that they correspond to couples of binary relations on A satisfying some conditions. If
is a directed partially ordered set, the only
with Int
isomorphic to Int
are
corresponding to direct decompositions
of
(
denotes the dual of
. The present results include those presented in the paper [11] by V. Slavík. Systems of intervals, particularly of lattices, have been investigated by many authors, cf. [1]–[11]. 相似文献
8.
Hiroshi Suzuki 《Journal of Algebraic Combinatorics》1998,7(2):165-180
It is well known that imprimitive P-polynomial association schemes
with
are either bipartite or antipodal, i.e., intersection numbers satisfy either
for all
for all
. In this paper, we show that imprimitive
-polynomial association schemes
with
are either dual bipartite or dual antipodal, i.e., dual intersection numbers satisfy either
. 相似文献
9.
A. È. Biryuk 《Functional Analysis and Its Applications》2001,35(1):1-12
We study the asymptotic behavior as
of the Sobolev norm
of the solution to the Cauchy problem for the one-dimensional quasilinear Burgers type equation
(It is assumed that the problem is
, the boundary conditions are periodic, and
.) We show that the locally time-averaged Sobolev norms satisfy the estimate
. The estimates obtained as a consequence for the Fourier coefficients justify Kolmogorov's spectral theory of turbulence for the case of the Burgers equation. 相似文献
10.
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
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.
D. M. Smirnov 《Algebra and Logic》2003,42(2):136-146
We continue to study interrelations between permutative varieties and the cyclic varieties defined by cycles of the form
. A criterion is given determining whether a cyclic variety
is interpretable in
. For a permutation
without fixed elements, it is stated that a set of primes
for which
is interpretable in
in the lattice
is finite. It is also proved that for distinct primes
, the Helly number of a type
in
coincides with dimension of the dual type
and equals
. 相似文献
13.
P. Véron 《Designs, Codes and Cryptography》2001,24(1):81-97
We compute in this paper the true dimension over
of Goppa Codes (L, g) defined by the polynomial
proving, this way, a conjecture stated in [14,16]. 相似文献
14.
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
15.
Suppose that k and l are integers such that
and
, M
k is a set of numbers without kth powers, and
. In this paper, we obtain asymptotic estimates of the sums
over
相似文献
16.
We prove a local limit theorem for large deviations of the sums
, where
, is a Markov Gaussian random field,
is a bounded vector-valued function, and
. This paper generalizes the paper [13]. 相似文献
17.
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
18.
Helena Ferreira 《Extremes》2000,3(4):385-392
Let
be a sequence of identically distributed variables. We study the asymptotic distribution of
, where Y
[r:n] denotes the concomitant of the rth order statistic X
r:n
, corresponding to
, and
is held fixed while
. Conditions are given for the
and
to have the same asymptotic behavior as that we would apply if
were i.i.d. The result is illustrated with a simple linear regression model
, where
is a stationary sequence with extremal index
. 相似文献
19.
We prove a theorem on possible test rank values for groups of the form
. It is shown that test rank of a free polynilpotent group
is equal to
or
, for any
and every collection
of classes. Moreover,
for
and
. 相似文献
20.
We construct the trajectory attractor
of a three-dimensional Navier--Stokes system with exciting force
. The set
consists of a class of solutions to this system which are bounded in
, defined on the positive semi-infinite interval
of the time axis, and can be extended to the entire time axis
so that they still remain bounded-in-
solutions of the Navier--Stokes system. In this case any family of bounded-in-
solutions of this system comes arbitrary close to the trajectory attractor
. We prove that the solutions
are continuous in t if they are treated in the space of functions ranging in
. The restriction of the trajectory attractor
to
,
, is called the global attractor of the Navier--Stokes system. We prove that the global attractor
thus defined possesses properties typical of well-known global attractors of evolution equations. We also prove that as
the trajectory attractors
and the global attractors
of the
-order Galerkin approximations of the Navier--Stokes system converge to the trajectory and global attractors
and
, respectively. Similar problems are studied for the cases of an exciting force of the form
depending on time
and of an external force
rapidly oscillating with respect to the spatial variables or with respect to time
. 相似文献