共查询到20条相似文献,搜索用时 31 毫秒
1.
Koji Momihara 《Designs, Codes and Cryptography》2007,45(3):379-390
A conflict-avoiding code (CAC) C of length n and weight k is a collection of k-subsets of such that holds for any , , where . A CAC with maximum code size for given n and k is called optimal. Furthermore, an optimal CAC C is said to be tight equi-difference if holds and any codeword has the form . The concept of a CAC is motivated from applications in multiple-access communication systems. In this paper, we give a
necessary and sufficient condition to construct tight equi-difference CACs of weight k = 3 and characterize the code length n’s admitting the condition through a number theoretical approach.
相似文献
2.
Maria Bras-Amorós 《Designs, Codes and Cryptography》2007,43(2-3):137-145
One-point codes are those algebraic-geometry codes for which the associated divisor is a non-negative multiple of a single
point. Evaluation codes were defined in order to give an algebraic generalization of both one-point algebraic-geometry codes
and Reed–Muller codes. Given an -algebra A, an order function on A and given a surjective -morphism of algebras , the ith evaluation code with respect to is defined as the code . In this work it is shown that under a certain hypothesis on the -algebra A, not only any evaluation code is a one-point code, but any sequence of evaluation codes is a sequence of one-point codes.
This hypothesis on A is that its field of fractions is a function field over and that A is integrally closed. Moreover, we see that a sequence of algebraic-geometry codes G
i
with associated divisors is the sequence of evaluation codes associated to some -algebra A, some order function and some surjective morphism with if and only if it is a sequence of one-point codes.
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3.
A probabilistic algorithm is presented for finding a basis of the root space of a linearized polynomial
over . The expected time complexity of the presented algorithm is O(n
t) operations in .
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4.
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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5.
Zhongwei Tang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2008,59(5):810-833
In this paper, we are concerned with the multiplicity of standing wave solutions of nonlinear Schr?dinger equations with electromagnetic
fields
for sufficiently large λ, where i is the imaginary unit, for N ≥ 3 and 2 < p < + ∞ for N = 1, 2. a(x) is a real continuous function on is such that A
j
(x) is a real local H?lder continuous function on for j = 1, 2, ... ,N. We assume that a(x) is nonnegative and has a potential well consisting of k components . We show that for any non-empty subset has a standing wave solution which is trapped in a neighborhood of for λ large.
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6.
Frédéric A. B. Edoukou 《Designs, Codes and Cryptography》2009,50(1):135-146
We study the functional codes of second order on a non-degenerate Hermitian variety as defined by G. Lachaud. We provide the best possible bounds for the number of points of quadratic sections of . We list the first five weights, describe the corresponding codewords and compute their number. The paper ends with two
conjectures. The first is about minimum distance of the functional codes of order h on a non-singular Hermitian variety . The second is about distribution of the codewords of first five weights of the functional codes of second order on a non-singular
Hermitian variety .
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7.
In 1960 Hughes and Kleinfeld (Am J Math 82:389–392, 1960) constructed a finite semifield which is two-dimensional over a weak
nucleus, given an automorphism σ of a finite field and elements with the property that has no roots in . In 1965 Knuth (J Algebra 2:182–217, 1965) constructed a further three finite semifields which are also two-dimensional over
a weak nucleus, given the same parameter set . Moreover, in the same article, Knuth describes operations that allow one to obtain up to six semifields from a given semifield.
We show how these operations in fact relate these four finite semifields, for a fixed parameter set, and yield at most five
non-isotopic semifields out of a possible 24. These five semifields form two sets of semifields, one of which consists of
at most two non-isotopic semifields related by Knuth operations and the other of which consists of at most three non-isotopic
semifields.
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8.
Valentina Pepe 《Designs, Codes and Cryptography》2007,42(3):303-315
In this paper, we study the code which has as parity check matrix the incidence matrix of the design of the Hermitian curve and its (q + 1)-secants. This code is known to have good performance with an iterative decoding algorithm, as shown by Johnson and Weller
in (Proceedings at the ICEE Globe com conference, Sanfrancisco, CA, 2003). We shall prove that has a double cyclic structure and that by shortening in a suitable way it is possible to obtain new codes which have higher code-rate. We shall also present a simple way to constructing the matrix
via a geometric approach.
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9.
John Polhill 《Designs, Codes and Cryptography》2009,52(2):163-169
By modifying a construction for Hadamard (Menon) difference sets we construct two infinite families of negative Latin square
type partial difference sets in groups of the form where p is any odd prime. One of these families has the well-known Paley parameters, which had previously only been constructed in
p-groups. This provides new constructions of Hadamard matrices and implies the existence of many new strongly regular graphs
including some that are conference graphs. As a corollary, we are able to construct Paley–Hadamard difference sets of the
Stanton-Sprott family in groups of the form when is a prime power. These are new parameters for such difference sets.
相似文献
10.
Let Γ6 be the elliptic curve of degree 6 in PG(5, q) arising from a non-singular cubic curve of PG(2, q) via the canonical Veronese embedding
(1) If Γ6 (equivalently ) has n
GF(q)-rational points, then the associated near-MDS code has length n and dimension 6. In this paper, the case q = 5 is investigated. For q = 5, the maximum number of GF(q)-rational points of an elliptic curve is known to be equal to ten. We show that for an elliptic curve with ten GF(5)-rational points, the associated near-MDS code can be extended by adding two more points of PG(5, 5). In this way we obtain six non-isomorphic [12, 6]5 codes. The automorphism group of is also considered.
相似文献
11.
Soogil Seo 《manuscripta mathematica》2008,127(3):381-396
A circular distribution is a Galois equivariant map ψ from the roots of unity μ
∞ to an algebraic closure of such that ψ satisfies product conditions, for ϵ ∈ μ
∞ and , and congruence conditions for each prime number l and with (l, s) = 1, modulo primes over l for all , where μ
l
and μ
s
denote respectively the sets of lth and sth roots of unity. For such ψ, let be the group generated over by and let be , where U
s
denotes the global units of . We give formulas for the indices and of and inside the circular numbers P
s
and units C
s
of Sinnott over .
This work was supported by the SRC Program of Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government
(MOST) (No. R11-2007-035-01001-0). This work was supported by the Korea Research Foundation Grant funded by the Korean Government
(MOEHRD, Basic Research Promotion Fund) (KRF-2006-312-C00455). 相似文献
12.
We derive the Singleton bound for poset codes and define the MDS poset codes as linear codes which attain the Singleton bound.
In this paper, we study the basic properties of MDS poset codes. First, we introduce the concept of I-perfect codes and describe the MDS poset codes in terms of I-perfect codes. Next, we study the weight distribution of an MDS poset code and show that the weight distribution of an MDS
poset code is completely determined. Finally, we prove the duality theorem which states that a linear code C is an MDS -code if and only if is an MDS -code, where is the dual code of C and is the dual poset of
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13.
We present a method for computing pth roots using a polynomial basis over finite fields of odd characteristic p, p ≥ 5, by taking advantage of a binomial reduction polynomial. For a finite field extension of our method requires p − 1 scalar multiplications of elements in by elements in . In addition, our method requires at most additions in the extension field. In certain cases, these additions are not required. If z is a root of the irreducible reduction polynomial, then the number of terms in the polynomial basis expansion of z
1/p
, defined as the Hamming weight of z
1/p
or , is directly related to the computational cost of the pth root computation. Using trinomials in characteristic 3, Ahmadi et al. (Discrete Appl Math 155:260–270, 2007) give is greater than 1 in nearly all cases. Using a binomial reduction polynomial over odd characteristic p, p ≥ 5, we find always.
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14.
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.
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15.
Miguel Ramos Hugo Tavares 《Calculus of Variations and Partial Differential Equations》2008,31(1):1-25
We consider a system of the form , in an open domain of , with Dirichlet conditions at the boundary (if any). We suppose that f and g are power-type non-linearities, having superlinear and subcritical growth at infinity. We prove the existence of positive
solutions and which concentrate, as , at a prescribed finite number of local minimum points of V(x), possibly degenerate. 相似文献
16.
In the study of the asymptotic behaviour of solutions of differential-difference equations the
-spectrum has been useful, where
and
implies Fourier transform
, with
given
, φ∈L
∞(ℝ,X), X a Banach space,
(half)line. Here we study
and related concepts, give relations between them, especially
weak Laplace half-line spectrum of φ, and thus ⊂ classical Beurling spectrum = Carleman spectrum =
; also
= Beurling spectrum of “φ modulo
” (Chill-Fasangova). If
satisfies a Loomis type condition (L
U
), then
countable and
uniformly continuous ∈U are shown to imply
; here (L
U
) usually means
, indefinite integral Pf of f in U imply Pf in
(the Bohl-Bohr theorem for
= almost periodic functions, U=bounded functions). This spectral characterization and other results are extended to unbounded functions via mean classes
, ℳ
m
U ((2.1) below) and even to distributions, generalizing various recent results for uniformly continuous bounded φ. Furthermore for solutions of convolution systems S*φ=b with
in some
we show
. With these above results, one gets generalizations of earlier results on the asymptotic behaviour of solutions of neutral
integro-differential-difference systems. Also many examples and special cases are discussed. 相似文献
17.
Let r
1, …, r
s
be non-zero integers satisfying r
1 + ⋯ + r
s
= 0. Let G be a finite abelian group with k
i
|k
i-1(2 ≤ i ≤ n), and suppose that (r
i
, k
1) = 1(1 ≤ i ≤ s). Let denote the maximal cardinality of a set which contains no non-trivial solution of r
1
x
1 + ⋯ + r
s
x
s
= 0 with . We prove that . We also apply this result to study problems in finite projective spaces.
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18.
We study self-dual codes over the rings
and
. We define various weights and weight enumerators over these rings and describe the groups of invariants for each weight enumerator over the rings. We examine the torsion codes over these rings to describe the structure of self-dual codes. Finally we classify self-dual codes of small lengths over
. 相似文献
19.
Arvind Singh 《Journal of Theoretical Probability》2007,20(2):153-166
We consider a diffusion process X in a random potential of the form , where is a positive drift and is a strictly stable process of index with positive jumps. Then the diffusion is transient and converges in law towards an exponential distribution. This behaviour contrasts with the case where is a drifted Brownian motion and provides an example of a transient diffusion in a random potential which is as “slow” as
in the recurrent setting.
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20.
Franc Forstnerič Björn Ivarsson Frank Kutzschebauch Jasna Prezelj 《Mathematische Annalen》2007,338(3):545-554
Given a Stein manifold x of dimension n > 1, a discrete sequence , and a discrete sequence where , there exists a proper holomorphic embedding satisfying f(a
j
) = b
j
for every j = 1,2,...
Forstnerič and Prezelj supported by grants P1-0291 and J1-6173, Republic of Slovenia.
Kutzschebauch supported by Schweizerische National fonds grant 200021-107477/1.
Ivarsson supported by The Wenner-Gren Foundations. 相似文献