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1.
Joseph H. Silverman 《Designs, Codes and Cryptography》2000,20(1):5-40
Let
be an elliptic curve defined over a finite field, and let
be two points on E. The Elliptic Curve Discrete Logarithm Problem (ECDLP) asks that an integer m be found so that S=mT in
. In this note we give a new algorithm, termed the Xedni Calculus, which might be used to solve the ECDLP. As remarked by Neal Koblitz, the Xedni method is also applicable to the classical discrete logarithm problem for
and to the integer factorization problem. 相似文献
2.
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
3.
We study lower bounds on K(n,R), the minimum number of codewords of any binary code of length n such that the Hamming spheres of radius R with center at codewords cover the Hamming space
. We generalize Honkala's idea toobtain further improvements only by using some simple observationsof Zhang's result. This leads to nineteen improvements of thelower bound on K(n,R) within the range of
. 相似文献
4.
We prove the absolute continuity of the spectrum of the Schrödinger operator in
,
, with periodic (with a common period lattice
) scalar
and vector
potentials for which either
,
, or the Fourier series of the vector potential
converges absolutely,
, where
is an elementary cell of the lattice
,
for
, and
for
, and the value of
is sufficiently small, where
and
otherwise,
, and
. 相似文献
5.
In the canonical smooth fiber bundles
endowed with the metric tensor fields of relevant structure, we consider natural representations of the Galilean groups
and construct
-invariant generalizations of differentiable connections. In both regular and special cases of the representations of the relevant groups
, we found all the affine nonholonomic
-,
-, and
-connections of the first order (see [1]–[3]) possessing the local Lie groups of transformations
and also described the respective
-invariant planar connections. 相似文献
6.
G. V. Kuz'mina 《Journal of Mathematical Sciences》2003,118(1):4880-4894
We apply a variant of the method of the extremal metric to some problems concerning extremal decompositions and related problems. Let
be a system of distinct points on
and let
be the family of all systems
of nonoverlapping simply connected domains on
such that
. Let
where
is the reduced module of the domain
with respect to the point
. At present, the problem concerning the value
was solved completely for
. In this work, we continue the previous author's investigations and consider the case
. In addition, we consider the problem concerning the maximum of the sum
in the family
introduced above, where
, are arbitrary points of the circle
, and is a positive number. We prove that if
, then the maximum is attained only for systems of equidistant points of the circle
. For
, this result was obtained earlier by Dubinin who applied the method of symmetrization. It is shown that if
, where
is an even number, then equidistant points of the circle
do not realize the indicated maximum. Bibliography: 11 titles. 相似文献
7.
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
8.
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
9.
Frédéric Paulin 《Geometriae Dedicata》2002,95(1):65-85
The aim of this paper is to give a geometric interpretation of the continued fraction expansion in the field
of formal Laurent series in X
–1 over
, in terms of the action of the modular group
on the Bruhat–Tits tree of
, and to deduce from it some corollaries for the diophantine approximation of formal Laurent series in X
–1 by rational fractions in X. 相似文献
10.
M. A. Shokrollahi 《Designs, Codes and Cryptography》1996,9(2):203-213
Let p be an odd prime and
be a primitive p th root of unity over
. The Galois group G of
over
is a cyclic group of order p-1. The integral group ring
[G] contains the Stickelberger ideal S
p
which annihilates the ideal class group of K. In this paper we investigate the parameters of cyclic codes S
p
(q) obtained as reductions of S
p
modulo primes q which we call Stickelberger codes. In particular, we show that the dimension of S
p
(p) is related to the index of irregularity of p, i.e., the number of Bernoulli numbers B
2k
,
, which are divisible by p. We then develop methods to compute the generator polynomial of S
p
(p). This gives rise to anew algorithm for the computation of the index of irregularity of a prime. As an application we show that 20,001,301 is regular. This significantly improves a previous record of 8,388,019 on the largest explicitly known regular prime. 相似文献
11.
We study the contact process in
d
and a family of two-parametric oriented percolation models in
d
×
+. It is proved that the derivative at the endpoint of the critical curve for percolation exists and its absolute value coincides with the critical rate for the corresponding contact process. 相似文献
12.
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
13.
Using an analog of the classical Frobenius recursion, we define the notion of a Frobenius
-homomorphism. For
, this is an ordinary ring homomorphism. We give a constructive proof of the following theorem. Let X be a compact Hausdorff space,
the
th symmetric power of X, and
the algebra of continuous complex-valued functions on X with the sup-norm; then the evaluation map
defined by the formula
identifies the space
with the space of all Frobenius
-homomorphisms of the algebra
into
with the weak topology. 相似文献
14.
Let
be a computable structure and let R be an additional relation on its domain. We establish a necessary and sufficient condition for the existence of an isomorphic copy
of
such that the image of R
is h-simple (h-immune) relative to
. 相似文献
15.
The 3-local geometry
of the sporadic simple group Co1 has been known to have a cover
with a flag-transitive automorphism group which is a nonsplit extension of an elementary Abelian 2-group of rank 24 (the Leech lattice modulo 2) by Co1. It was conjectured that
was simply connected. We disprove this conjecture by constructing a double cover
of
. The automorphism group of
is of the shape
. However, it is not isomorphic to the involution centralizer of the Monster sporadic simple group. 相似文献
16.
In this paper, the boundedness of the Riesz potential generated by generalized shift operator
from the spaces
to the spaces
is examined. 相似文献
17.
H. Renelt 《Journal of Mathematical Sciences》2003,115(2):2251-2261
By means of an elementary consideration, families of integral transformations in certain spaces (e.g., in
, where
is the unit disk) are constructed. These transformations map elements of certain subspaces either to itself or to their derivatives, respectively. As a special case, we obtain a family of integral transformations generating a decomposition of
into a direct sum. By introducing appropriate new scalar products, these direct sums become decompositions into orthogonal complements, and the corresponding integral transformations become self-adjoint operators of
into itself positive with respect to the new scalar products. In further special cases, these integral transformations possess bounded and injective extensions mapping
onto well-defined subspaces of
. The latter property is a consequence of the connection of our transformations with the complex Hilbert transformation. Bibliography: 10 titles. 相似文献
18.
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
19.
Thomas Geisser 《K-Theory》1997,12(3):193-226
We prove that for W2
the Witt vectors of length two over the finite field
, we have
in characteristic at least 5 and
for (3,f) = 1. The result is proved by using the identity
and calculating the right term with a group homology spectral sequence. Some information on the spectral sequence is achieved by using the action of the outer automorphism of SL on the homology groups and recent results on K-groups of local rings and the ring of dual numbers over finite fields. 相似文献
20.
Wiesław Śliwa 《Czechoslovak Mathematical Journal》2004,54(2):457-463
We prove that any infinite-dimensional non-archimedean Fréchet space E is homeomorphic to
where D is a discrete space with card(D) = dens(E). It follows that infinite-dimensional non-archimedean Fréchet spaces E and F are homeomorphic if and only if dens(E) = dens(F). In particular, any infinite-dimensional non-archimedean Fréchet space of countable type over a field
is homeomorphic to the non-archimedean Fréchet space
. 相似文献