共查询到20条相似文献,搜索用时 46 毫秒
1.
Dose Valerio Mercuri Pietro Pal Ankan Stirpe Claudio 《Designs, Codes and Cryptography》2022,90(6):1347-1368
Designs, Codes and Cryptography - We illustrate a general technique to construct towers of fields producing high order elements in $$\mathbb {F}_{q^{2^n}}$$ , for odd q, and in $$\mathbb {F}_{2^{2... 相似文献
2.
3.
José Joaquín Bernal Ángel del Río Juan Jacobo Simón 《Designs, Codes and Cryptography》2009,51(3):289-300
A (left) group code of length n is a linear code which is the image of a (left) ideal of a group algebra via an isomorphism which maps G to the standard basis of . Many classical linear codes have been shown to be group codes. In this paper we obtain a criterion to decide when a linear
code is a group code in terms of its intrinsical properties in the ambient space , which does not assume an “a priori” group algebra structure on . As an application we provide a family of groups (including metacyclic groups) for which every two-sided group code is an
abelian group code. It is well known that Reed–Solomon codes are cyclic and its parity check extensions are elementary abelian
group codes. These two classes of codes are included in the class of Cauchy codes. Using our criterion we classify the Cauchy
codes of some lengths which are left group codes and the possible group code structures on these codes.
Research supported by D.G.I. of Spain and Fundación Séneca of Murcia. 相似文献
4.
Carles Bivià-Ausina 《Mathematische Zeitschrift》2007,257(4):745-767
In this paper we give a lower bound for the Łojasiewicz exponent at infinity of a special class of polynomial maps , s ≥ 1. As a consequence, we detect a class of polynomial maps that are global diffeomorphisms if their Jacobian determinant never vanishes.
Work supported by DGICYT Grant BFM2003–02037/MATE. 相似文献
5.
6.
Yu. I. Lyubich 《Designs, Codes and Cryptography》2009,51(1):21-31
It is shown that among all tight designs in , where is or , or (quaternions), only 5-designs in (Lyubich, Shatalora Geom Dedicata 86: 169–178, 2001) have irrational angle set. This is the only case of equal ranks of the
first and the last irreducible idempotent in the corresponding Bose-Mesner algebra.
相似文献
7.
Timothy Logvinenko 《Mathematische Annalen》2008,341(1):137-167
In most cases where it has been shown to exist the derived McKay correspondence can be written as a Fourier–Mukai transform which sends point sheaves of the crepant resolution Y to pure sheaves in . We give a sufficient condition for to be the defining object of such a transform. We use it to construct the first example of the derived McKay correspondence
for a non-projective crepant resolution of . Along the way we extract more geometrical meaning out of the Intersection Theorem and learn to compute θ-stable families of G-constellations and their direct transforms. 相似文献
8.
Designs, Codes and Cryptography - In this work, we study functions that can be obtained by restricting a vectorial Boolean function $$F :\mathbb {F}_{2}^n \rightarrow \mathbb {F}_{2}^n$$ to an... 相似文献
9.
Designs, Codes and Cryptography - Let $${\mathbb F}_{q}$$ be a finite field of size q and $${\mathbb F}_{q}^*$$ the set of non-zero elements of $${\mathbb F}_{q}$$ . In this paper, we study a class... 相似文献
10.
Mathematical Notes - Let $$\mathbb{F}_{q}$$ be a finite field, let $$\mathbb{X}$$ be a subset of the projective space ?s?1 over $$\mathbb{F}_{q}$$ parametrized by rational functions,... 相似文献
11.
ALAIN HÉNAUT 《Geometriae Dedicata》1997,65(1):89-101
A d-web in (
,0) is given by d complex analytic foliations of codimension one in (
,0) which are in general position. A d-web
in (
,0) is linear if all the leaves are (pieces of) hyperplanes in
and
is algebraic if it is associated, by duality, to a nondegenerate algebraic curve in
of degree d. We characterize linear webs in (
,0). We give explicit conditions under which a linear d-web in (
,0) is algebraic and we obtain equations for
in this case. Some related problems are discussed and some questions are posed. 相似文献
12.
Let H1(
) be the usual Hardy space on
. We show that the couple (H1(
), L(
) is a Calderón couple. This result immediately follows from the following stronger one: Given any fH1(
) +L(
) there exist two linear operators U and V satisfying the properties: (i) Uf=Nf (Nf being the non-tangential maximal function of f) and U is contractive from H1(
) to L1(
) and also from L(
) to L(
); (ii) V(Nf)=f, V is similtaneously bounded from L1(
) to H1(
) and from L(
) to L(
) and the norms of V on these spaces are controlled by a universal constant. We also have similar results on the couple (Lp(
), BMO (
)) for every 1
相似文献
13.
Hans-Peter Schröcker 《Journal of Geometry》2005,82(1-2):172-187
We study the projective space
of univariate rational parameterized equations of degree d or less in real projective space
The parameterized equations of degree less than d form a special algebraic variety
We investigate the subspaces on
and their relation to rational curves in
give a geometric characterization of the automorphism group of
and outline applications of the theory to projective kinematics. 相似文献
14.
An (n,k)-affine source over a finite field is a random variable X = (X
1,..., X
n
) ∈ , which is uniformly distributed over an (unknown) k-dimensional affine subspace of . We show how to (deterministically) extract practically all the randomness from affine sources, for any field of size larger
than n
c
(where c is a large enough constant). Our main results are as follows:
Research supported by Israel Science Foundation (ISF) grant. 相似文献
1. | (For arbitrary k): For any n,k and any of size larger than n 20, we give an explicit construction for a function D : → , such that for any (n,k)-affine source X over , the distribution of D(X) is ∊-close to uniform, where ∊ is polynomially small in ||. |
2. | (For k=1): For any n and any of size larger than n c , we give an explicit construction for a function D: , such that for any (n, 1)-affine source X over , the distribution of D(X) is ∊-close to uniform, where ∊ is polynomially small in ||. Here, δ>0 is an arbitrary small constant, and c is a constant depending on δ. |
15.
Journal of Algebraic Combinatorics - The fact that the groups $${\mathbb {Z}}_{2^m} \times {\mathbb {Z}}_{2^m}$$ contain difference sets was first established by induction by Jim Davis in his... 相似文献
16.
We prove the absence of positive eigenvalues of Schrödinger operators
$ H=-\Delta+V $ on Euclidean spaces $ \mathbb{R}^n $ for a certain class of rough
potentials $V$. To describe our class of potentials fix an exponent
$q\in[n/2,\infty]$ (or $q\in(1,\infty]$, if $n=2$) and let $\beta(q)=(2q-n)/(2q)$.
For the potential $V$ we assume that $V\in L^{n/2}_{{\rm{loc}}}(\mathbb{R}^n)$
(or $V\in L^{r}_{{\rm{loc}}}(\mathbb{R}^n)$, $r>1$, if $n=2$) and$\begin{equation*}$$\lim_{R\to\infty}R^{\beta(q)}||V||_{L^q(R\leq |x|\leq 2R)}=0\,.$$\end{equation*}$Under these assumptions we prove that the operator $H$ does not
admit positive eigenvalues. The case $q=\infty$ was considered by Kato [K].
The absence of positive eigenvalues follows from a uniform Carleman
inequality of the form$\begin{equation*}$$||W_m u||_{l^a(L^{p(q)})(\mathbb R^n)}\leq C_q||W_m|x|^{\beta(q)}(\Delta+1)u||_{l^a(L^{p(q)})(\mathbb{R}^n)}$$\end{equation*}$for all smooth compactly supported functions $u$ and a suitable sequence of weights $W_m$,
where $p(q)$ and $p(q)$ are dual exponents with the property that $1/p(q)-1/p(q)=1/q$. 相似文献
17.
Summary.
Let
We say that
preserves the distance d 0 if
for each
implies
Let A
n
denote the set of all positive numbers
d such that any map
that preserves unit distance preserves also distance
d.
Let D
n
denote the set of all positive numbers
d with the property: if
and
then there exists a finite set
S
xy
with
such that any map
that preserves unit distance preserves also the distance between
x and y.
Obviously,
We prove:
(1)
(2)
for n 2
D
n
is a
dense subset of
(2) implies that each mapping
f
from
to
(n 2)
preserving unit distance preserves all distances,
if f is continuous with respect to the product topologies
on
and
相似文献
18.
Let
be a family of unit balls in
with the property that the mutual distances of the centers are at least
. If any n2 members of
have a common line transversal, then
has a line transversal too.
Received: 27 January 2005; revised: 17 October 2005 相似文献
19.
Cesar Enrique Torres Ledesm Ziheng Zhang Amado Mendez 《Journal of Applied Analysis & Computation》2019,9(6):2436-2453
We study the existence of solutions for the following fractional Hamiltonian systems
$$
\left\{
\begin{array}{ll}
- _tD^{\alpha}_{\infty}(_{-\infty}D^{\alpha}_{t}u(t))-\lambda L(t)u(t)+\nabla W(t,u(t))=0,\\[0.1cm]
u\in H^{\alpha}(\mathbb{R},\mathbb{R}^n),
\end{array}
\right.
~~~~~~~~~~~~~~~~~(FHS)_\lambda
$$
where $\alpha\in (1/2,1)$, $t\in \mathbb{R}$, $u\in \mathbb{R}^n$, $\lambda>0$ is a parameter, $L\in C(\mathbb{R},\mathbb{R}^{n^2})$ is a symmetric matrix, $W\in C^1(\mathbb{R} \times \mathbb{R}^n,\mathbb{R})$. Assuming that
$L(t)$ is a positive semi-definite symmetric matrix, that is, $L(t)\equiv 0$ is allowed to occur in some finite interval $T$ of $\mathbb{R}$,
$W(t,u)$ satisfies some superquadratic conditions weaker than Ambrosetti-Rabinowitz condition, we show that (FHS)$_\lambda$ has a solution which vanishes on
$\mathbb{R}\setminus T$ as $\lambda \to \infty$, and converges to some $\tilde{u}\in H^{\alpha}(\R, \R^n)$. Here, $\tilde{u}\in E_{0}^{\alpha}$ is a solution
of the Dirichlet BVP for fractional systems on the finite interval $T$. Our results are new and improve recent results in the literature even in the case $\alpha =1$. 相似文献
20.
This paper investigates the number of trace-one elements in a polynomial basis for
. A polynomial basis with a small number of trace-one elements is desirable because it results in an efficient and low cost
implementation of the trace function. We focus on the case where the reduction polynomial is a trinomial or a pentanomial,
in which case field multiplication can also be efficiently implemented.
Communicated by: P. Wild 相似文献