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1.
Let Q denote the field of rational numbers. Let K be a cyclic quartic extension of Q. It is known that there are unique integers A, B, C, D such that
where A is squarefree and odd, D=B
2+C
2 is squarefree, B
$$
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0 , C
$$
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0, GCD(A,D)=1. The conductor f(K) of K is f(K) = 2
l
|A|D, where
A simple proof of this formula for f(K) is given, which uses the basic properties of quartic Gauss sums. 相似文献
2.
A Kirkman packing design KPD ({3, 5*},v) is a resolvable packing with maximum possible number of parallel classes, each class containing one block of size 5 and all other blocks of size three. Such designs can be used to construct certain threshold schemes in cryptography. In this paper, direct and recursive constructions are discussed for such designs. The existence of a KPD ({3, 5*},v) for
is established with a few possible exceptions. 相似文献
3.
Marco Buratti 《Designs, Codes and Cryptography》1999,16(2):117-120
We give the explicit construction of a regular (17q, 17, 2)-BIBD for any prime power q 17 (mod 32) such that 2 is not a 4th power in GF(q) and the explicit construction of a regular (25q, 25, 3)-BIBD for any prime power q 25 (mod 48) such that
and
+3 are non-squares in GF(q). 相似文献
4.
An n-subsetD of a group G of order
is called an affine difference set of G relativeto a normal subgroup N of G of order
if the list of differences
containseach element of G-N exactly once and no elementof N. It is a well-known conjecture that if Dis an affine difference set in an abelian group G,then for every prime p, the Sylow p-subgroupof G is cyclic. In Arasu and Pott [1], it was shownthat the above conjecture is true when
. In thispaper we give some conditions under which the Sylow p-subgroupof G is cyclic. 相似文献
5.
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
6.
M. S. Lyapina 《Journal of Mathematical Sciences》2004,120(2):1109-1116
A bi-Lipschitz continuous mapping of a space X is a bijection
such that
, where
. We write
if f is a Lipschitz (bi-Lipschitz) mapping of X into itself and denote by
the set of all bi-Lipschitz mappings of X that are not isometry. Thus,
if
and blip
. For X we consider a standard Cantor set K on the real line (with standard metric). The main result of this paper is formulated as follows:
where
Bibliography: 2 titles. 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.
A (k,n)-arc in PG(2,q) is usually defined to be a set
of k points in the plane such that some line meets
in n points but such that no line meets
in more than n points. There is an extensive literature on the topic of (k,n)-arcs. Here we keep the same definition but allow
to be a multiset, that is, permit
to contain multiple points. The case k=q
2+q+2 is of interest because it is the first value of k for which a (k,n)-arc must be a multiset. The problem of classifying (q
2+q+2,q+2)-arcs is of importance in coding theory, since it is equivalent to classifying 3-dimensional q-ary error-correcting codes of length q
2+q+2 and minimum distance q
2. Indeed, it was the coding theory problem which provided the initial motivation for our study. It turns out that such arcs are surprisingly rich in geometric structure. Here we construct several families of (q
2+q+2,q+2)-arcs as well as obtain some bounds and non-existence results. A complete classification of such arcs seems to be a difficult problem. 相似文献
9.
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
10.
Blessilda P. Raposa 《Designs, Codes and Cryptography》2001,23(1):35-52
We determine here some possible values for thecardinality of the intersection of three blocks from Paley2-(2q+1, q, (q-1)/2) designs where qis a prime power such that
(mod 4). 相似文献
11.
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
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.
John B. Polhill 《Designs, Codes and Cryptography》2002,25(3):299-309
There have been several recent constructions of partial difference sets (PDSs) using the Galois rings
for p a prime and t any positive integer. This paper presents constructions of partial difference sets in
where p is any prime, and r and t are any positive integers. For the case where
2$$
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many of the partial difference sets are constructed in groups with parameters distinct from other known constructions, and the PDSs are nested. Another construction of Paley partial difference sets is given for the case when p is odd. The constructions make use of character theory and of the structure of the Galois ring
, and in particular, the ring
×
. The paper concludes with some open related problems. 相似文献
14.
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
15.
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
16.
The paper is devoted to the study of the similarity to self-adjoint operators of operators of the form
, in the space
with weight
. As is well known, the answer to this problem in the case
is positive; it was obtained by using delicate methods of the theory of Hilbert spaces with indefinite metric. The use of a general similarity criterion in combination with methods of perturbation theory for differential operators allows us to generalize this result to a much wider class of weight functions
. 相似文献
17.
For a Hopf algebra
, we define the structures of differential complexes on two dual exterior Hopf algebras: (1) an exterior extension of
and (2) an exterior extension of the dual algebra
*. The Heisenberg double of these two exterior Hopf algebras defines the differential algebra for the Cartan differential calculus on
. The first differential complex is an analogue of the de Rham complex. When
* is a universal enveloping algebra of a Lie (super)algebra, the second complex coincides with the standard complex. The differential is realized as an (anti)commutator with a BRST operator Q. We give a recursive relation that uniquely defines the operator Q. We construct the BRST and anti-BRST operators explicitly and formulate the Hodge decomposition theorem for the case of the quantum Lie algebra U
q(gl(N)). 相似文献
18.
Let
be the prime factorization of a positive integer k and let b
k
(n) denote the number of partitions of a non-negative integer n into parts none of which are multiples of k. If M is a positive integer, let S
k
(N; M) be the number of positive integers N for which b
k(n
) 0(mod
M). If
we prove that, for every positive integer j
In other words for every positive integer j,
b
k(n) is a multiple of
for almost every non-negative integer n. In the special case when k=p is prime, then in representation-theoretic terms this means that the number ofp -modular irreducible representations of almost every symmetric groupS
n is a multiple of p
j. We also examine the behavior of b
k(n) (mod
) where the non-negative integers n belong to an arithmetic progression. Although almost every non-negative integer n (mod t) satisfies b
k(n) 0 (mod
), we show that there are infinitely many non-negative integers n r (mod t) for which b
k(n) 0 (mod
) provided that there is at least one such n. Moreover the smallest such n (if there are any) is less than 2
. 相似文献
19.
Qi S. Zhang 《Journal of Computational Analysis and Applications》2000,2(4):277-292
We study the inhomogeneous semilinear wave equations
on
with initial values
and
,where
is a noncompact, complete manifold. We founda new critical behavior in the following sense. There exists ap* > 0. When 1 < p p*, the above problem hasno global solution for any nonnegative
not identicallyzero and for any
and
; when
the problem has a global solution for some
and some
and
. If
, which is equipped with the Euclideanmetric, then
. If
we show that
belongs to the blow upcase. Although homogeneous semilinear wave equations are known to exhibit acritical behavior for a long time, this seems to be the first result oninhomogeneous ones. 相似文献
20.
Kh. D. Ikramov 《Journal of Mathematical Sciences》2004,121(4):2458-2464
A matrix
is said to be accretive-dissipative if, in its Hermitian decomposition
, both matrices B and C are positive definite. Further, if B= I
n, then A is called a Buckley matrix. The following extension of the classical Fischer inequality for Hermitian positive-definite matrices is proved. Let
be an accretive-dissipative matrix, k and l be the orders of A
11 and A
22, respectively, and let m = min{k,l}. Then
For Buckley matrices, the stronger bound
is obtained. Bibliography: 5 titles. 相似文献