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1.
Gerzson Kéri 《Designs, Codes and Cryptography》2008,46(2):191-198
The covering radius of binary 2-surjective codes of maximum length is studied in the paper. It is shown that any binary 2-surjective
code of M codewords and of length has covering radius if M − 1 is a power of 2, otherwise . Two different combinatorial proofs of this assertion were found by the author. The first proof, which is written in the
paper, is based on an existence theorem for k-uniform hypergraphs where the degrees of its vertices are limited by a given upper bound. The second proof, which is omitted
for the sake of conciseness, is based on Baranyai’s theorem on l-factorization of a complete k-uniform hypergraph.
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2.
For a subset ψ of PG(N, 2) a known result states that ψ has polynomial degree ≤ r, r≤ N, if and only if ψ intersects every r-flat of PG(N, 2) in an odd number of points. Certain refinements of this result are considered, and are then applied in the case when
ψ is the Grassmannian
, to show that for n <8 the polynomial degree of
is
. 相似文献
3.
We determine the minimum length n
q
(k, d) for some linear codes with k ≥ 5 and q ≥ 3. We prove that n
q
(k, d) = g
q
(k, d) + 1 for when k is odd, for when k is even, and for .
This work was supported by the Korea Research Foundation Grant funded by the Korean Government(MOEHRD). (KRF-2005-214-C00175).
This research has been partially supported by Grant-in-Aid for Scientific Research of Japan Society for the Promotion of Science
under Contract Number 17540129. 相似文献
4.
We prove that every [n, k, d]
q
code with q ≥ 4, k ≥ 3, whose weights are congruent to 0, −1 or −2 modulo q and is extendable unless its diversity is for odd q, where .
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5.
Thomas Westerbäck 《Designs, Codes and Cryptography》2007,42(3):335-355
A maximal partial Hamming packing of is a family of mutually disjoint translates of Hamming codes of length n, such that any translate of any Hamming code of length n intersects at least one of the translates of Hamming codes in . The number of translates of Hamming codes in is the packing number, and a partial Hamming packing is strictly partial if the family does not constitute a partition of .
A simple and useful condition describing when two translates of Hamming codes are disjoint or not disjoint is proved. This
condition depends on the dual codes of the corresponding Hamming codes. Partly, by using this condition, it is shown that
the packing number p, for any maximal strictly partial Hamming packing of , n = 2
m
−1, satisfies .
It is also proved that for any n equal to 2
m
−1, , there exist maximal strictly partial Hamming packings of with packing numbers n−10,n−9,n−8,...,n−1. This implies that the upper bound is tight for any n = 2
m
−1, .
All packing numbers for maximal strictly partial Hamming packings of , n = 7 and 15, are found by a computer search. In the case n = 7 the packing number is 5, and in the case n = 15 the possible packing numbers are 5,6,7,...,13 and 14.
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6.
We determine exact values for the k-error linear complexity L
k
over the finite field
of the Legendre sequence
of period p and the Sidelnikov sequence
of period p
m
− 1. The results are
for 1 ≤ k ≤ (p
m
− 3)/2 and
for k≥ (p
m
− 1)/2. In particular, we prove
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7.
Steven D. Taliaferro Lei Zhang 《Calculus of Variations and Partial Differential Equations》2006,26(4):401-428
We give conditions on a positive Hölder continuous function C2such that every C
2 positive solution u((x)) of the conformal scalar curvature equation
in a punctured neighborhood of the origin in R
n
either has a removable singularity at the origin or satisfies
for some positive singular solution u
0(|x|) of
where is the Hölder exponent of K.Mathematics Subject Classification (2000) Primary 35J60, 53C21 相似文献
8.
Jean-Paul Bézivin 《manuscripta mathematica》2008,126(1):41-47
Résumé Let with |q| > 1, and a be a rational number such that a
2 is not equal to for . In this note, we prove that the sum is irrational. 相似文献
9.
Yan Yaqiang 《Southeast Asian Bulletin of Mathematics》2002,25(4):769-782
We introduce some practical calculation of the weakly convergent sequence coefficients of Orlicz sequence spaces equipped with Luxemburg norm and Orlicz norm. For the N-function (u) of which the index function is monotonuous, the exact value WCS(l()) of Orlicz sequence space l() with Luxemburg norm is available, i.e. WCS(l()) =
or
WCS(l) of l with Orlicz norm has the exact value
or estimation
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10.
Let p be a prime and let be an elliptic curve defined over the finite field of p elements. For a given point the linear congruential genarator on elliptic curves (EC-LCG) is a sequence (U
n
) of pseudorandom numbers defined by the relation: where denote the group operation in and is the initial value or seed. We show that if G and sufficiently many of the most significants bits of two consecutive values U
n
, U
n+1 of the EC-LCG are given, one can recover the seed U
0 (even in the case where the elliptic curve is private) provided that the former value U
n
does not lie in a certain small subset of exceptional values. We also estimate limits of a heuristic approach for the case
where G is also unknown. This suggests that for cryptographic applications EC-LCG should be used with great care. Our results are
somewhat similar to those known for the linear and non-linear pseudorandom number congruential generator.
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11.
Jean-Christophe Bourgoin 《Annals of Global Analysis and Geometry》2007,32(1):1-13
In this paper, we study the minimality of the map for the weighted energy functional , where is a continuous function. We prove that for any integer and any non-negative, non-decreasing continuous function f, the map minimizes E
f,p
among the maps in which coincide with on . The case p = 1 has been already studied in [Bourgoin J.-C. Calc. Var. (to appear)]. Then, we extend results of Hong (see Ann. Inst.
Poincaré Anal. Non-linéaire 17: 35–46 (2000)). Indeed, under the same assumptions for the function f, we prove that in dimension n ≥ 7 for any real with , the map minimizes E
f,p
among the maps in which coincide with on .
相似文献
12.
Stamatis Koumandos 《Numerical Algorithms》2007,44(3):249-253
Motivated by work on positive cubature formulae over the spherical surface, Gautschi and Leopardi conjectured that the inequality
holds for α,β > − 1 and n ≥ 1, θ ∈ (0, π), where are the Jacobi polynomials of degree n and parameters (α, β). We settle this conjecture in the special cases where .
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13.
In a previous paper, we have obtained a characterization of the binary bent functions on (GF(2))n (n even) as linear combinations modulo
, with integral coefficients, of characteristic functions (indicators) of
-dimensional vector-subspaces of (GF(2))n. There is no uniqueness of the representation of a given bent function related to this characterization. We obtain now a new characterization for which there is uniqueness of the representation. 相似文献
14.
Jackson and Watts (J Econ Theory 71: 44–74, 2002) have examined the dynamic formation and stochastic evolution of networks. We provide a refinement of pairwise stability, p-pairwise stability, which allows us to characterize the stochastically stable networks without requiring the “tree construction” and the computation of resistance that may be quite complex. When a
-pairwise stable network exists, it is unique and it coincides with the unique stochastically stable network. To solve the inexistence problem of p-pairwise stable networks, we define its set-valued extension with the notion of p-pairwise stable set. The
-pairwise stable set exists and is unique. Any stochastically stable networks is included in the
-pairwise stable set. Thus, any network outside the
-pairwise stable set must be considered as a non-robust network. We also show that the
-pairwise stable set can contain no pairwise stable network and we provide examples where a set of networks is more “stable” than a pairwise stable network. 相似文献
15.
In this paper we examine whether the number of pairwise non-isomorphic minimal blocking sets in PG(2, q) of a certain size is larger than polynomial. Our main result is that there are more than polynomial pairwise non-isomorphic
minimal blocking sets for any size in the intervals [2q−1, 3q−4] for q odd and for q square. We can also prove a similar result for certain values of the intervals and .
相似文献
16.
P. M. Akhmet’ev 《Journal of Mathematical Sciences》2009,159(6):761-776
We present an approach to the Kervaire-invariant-one problem. The notion of the geometric (ℤ/2 ⨁ ℤ/2)-control of self-intersection of a skew-framed immersion and the notion of the (ℤ/2 ⨁ ℤ/4)-structure on the self-intersection manifold of a D
4-framed immersion are introduced. It is shown that a skew-framed immersion ↬ℝ
n
, 0 < q ≪ n (in the -range), admits a geometric (ℤ/2 ⨁ ℤ/2)-control if the characteristic class of the skew-framing of this immersion admits a retraction of order q, i.e., there exists a mapping such that this composition → ℝP∞ is the characteristic class of the skew-framing of f. Using the notion of (ℤ/2 ⨁ ℤ/2)-control, we prove that for a sufficiently large n, n = 2
l
− 2, an arbitrarily immersed D
4-framed manifold admits in the regular cobordism class (modulo odd torsion) an immersion with a (ℤ/2 ⨁ ℤ/4)-structure.
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 8, pp. 17–41, 2007. 相似文献
17.
Let G: = G(1,n,q) denote the Grassmannian of lines in PG(n,q), embedded as a point-set in PG(N, q) with
For n = 2 or 3 the characteristic function
of the complement of G is contained in the linear code generated by characteristic functions of complements of n-flats in PG(N, q). In this paper we prove this to be true for all cases (n, q) with q = 2 and we conjecture this to be true for all remaining cases (n, q). We show that the exact polynomial degree of
is
for δ: = δ(n, q) = 0 or 1, and that the possibility δ = 1 is ruled out if the above conjecture is true. The result deg(
for the binary cases (n,2) can be used to construct quantum codes by intersecting G with subspaces of dimension at least
相似文献
18.
Maximum nonlinear functions are widely used in cryptography because the coordinate functions F
β
(x) := tr(β
F(x)), , have large distance to linear functions. Moreover, maximum nonlinear functions have good differential properties, i.e.
the equations F(x + a) − F(x) = b, , have 0 or 2 solutions. Two classes of maximum nonlinear functions are the Gold power functions , gcd(k, m) = 1, and the Kasami power functions , gcd(k, m) = 1. The main results in this paper are: (1) We characterize the Gold power functions in terms of the distance of their
coordinate functions to characteristic functions of subspaces of codimension 2 in . (2) We determine the differential properties of the Kasami power functions if gcd(k,m) ≠ 1.
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19.
We prove the following statement.
Let , and let . Suppose that, for all and , the sequence satisfies the relation
where e(u) : = e2πiu
.
Then
where
q is the set of q-multiplicative functions g such that . 相似文献
20.
Alina Sîntămărian 《Numerical Algorithms》2007,46(2):141-151
The purpose of this paper is to evaluate the limit γ(a) of the sequence , where a ∈ (0, + ∞ ).
相似文献