Multi-sequences with d-perfect property

Sequences with almost perfect linear complexity profile are defined by Niederreiter (Proceedings of the Salzburg Conference 1986, Vol. 5, Teubner, Stuttgart, 1987, pp. 221–233). Xing and Lam (IEEE Trans. Inform. Theory 45 (1999) 1267; J. Complexity 16 (2000) 661) extended this concept from the case of single sequences to the case of multi-sequences and further proposed the concept of d-perfect multi-sequences. In this paper, based on the technique of m-continued fractions due to Dai et al. we investigate the property of d-perfect multi-sequences and obtain a sufficient and necessary condition of d-perfect multi-sequences. We show that d-perfect multi-sequences are not always strongly d-perfect. In particular, we give an example to disprove the conjecture proposed by Xing (2000) on d-perfect multi-sequences.     

基于代数曲线上具有高广义联合线性复杂度的多重序列

多重序列的联合线性复杂度是衡量基于字的流密码体系安全的一个重要指标. 由元素取自F_q上的m 重序列和元素取自F_q^m 上的单个序列之间的一一对应, Meidl 和Özbudak 定义多重序列的广义联合线性复杂度为对应的单个序列的线性复杂度. 在本文中, 我们利用代数曲线的常数域扩张, 研究两类多重序列的广义联合线性复杂度. 更进一步, 我们指出这两类多重序列同时具有高联合线性复杂度和高广义联合线性复杂度.     

Solving the FCSR synthesis problem for multi-sequences by lattice basis reduction

Register synthesis for multi-sequences has significance for the security of word-oriented stream ciphers. Feedback with carry shift registers (FCSRs) are promising alternatives to linear feedback shift registers for the design of stream ciphers. In this paper, we solve the FCSR synthesis problem for multi-sequences by two rational approximation algorithms using lattice theory. One is based on the lattice reduction greedy algorithm proposed by Nguyen and Stehlé (ACM Trans Algorithms (TALG) 5(4):46, 2009). The other is based on the LLL algorithm which is a polynomial time lattice reduction algorithm. Both of these rational approximation algorithms can find the smallest common FCSR for a given multi-sequence but with different numbers of known terms. When the number of sequences within the multi-sequence is less than or equal to 3, the former is suggested because it has better time complexity and fewer terms are needed. Otherwise, the latter will have better time complexity.     

On the joint linear complexity profile of explicit inversive multisequences

We prove lower bounds on the joint linear complexity profile of multisequences obtained by explicit inversive methods and show that for some suitable choices of parameters these joint linear complexity profiles are close to be perfect.     

Binary linear codes from vectorial boolean functions and their weight distribution

Binary linear codes with good parameters have important applications in secret sharing schemes, authentication codes, association schemes, and consumer electronics and communications. In this paper, we construct several classes of binary linear codes from vectorial Boolean functions and determine their parameters, by further studying a generic construction developed by Ding et al. recently. First, by employing perfect nonlinear functions and almost bent functions, we obtain several classes of six-weight linear codes which contain the all-one codeword, and determine their weight distribution. Second, we investigate a subcode of any linear code mentioned above and consider its parameters. When the vectorial Boolean function is a perfect nonlinear function or a Gold function in odd dimension, we can completely determine the weight distribution of this subcode. Besides, our linear codes have larger dimensions than the ones by Ding et al.’s generic construction.     

On improved asymptotic bounds for codes from global function fields

We analyse a binary cyclotomic sequence constructed via generalized cyclotomic classes by Bai et al. (IEEE Trans Inforem Theory 51: 1849–1853, 2005). First we determine the linear complexity of a natural generalization of this binary sequence to arbitrary prime fields. Secondly we consider k-error linear complexity and autocorrelation of these sequences and point out certain drawbacks of this construction. The results show that the parameters for the sequence construction must be carefully chosen in view of the respective application.      

Linear analysis and energy budget of viscous liquid jets in both axial and radial electric fields

In their countless industrial applications, axisymmetric and non-axisymmetric instabilities are respectively responsible for electrospraying and electrospinning. A linear method and energy budget have been applied in this study to investigate the instability of viscous jets under both the axial and radial electric fields; the liquid was taken to be a leaky dielectric and the gas a perfect dielectric; the effect of a parabolic velocity profile was considered and compared to that of a uniform velocity, and the energy analysis explained the physical mechanisms to an extent. The liquid viscosity and parabolic velocity profile had a combined effect on jet instability. Work induced by the parabolic velocity profile consisted of two parts: the energy transferred from the basic flow to the disturbances, and the influence of the corresponding shear stresses. At low viscosities, these influences were positive enough to prevail over the viscous dissipation, enhancing axisymmetric instability. However, the parabolic velocity profile functioned differently in small and large wavenumber regions, and the response to the axial electric fields varied in different regions, accounting for the dual effects of axial electric fields on axisymmetric instability. Also, under the interplay between the strong axial electric fields and the parabolic velocity profile, two distinct unstable regions emerged for the non-axisymmetric mode. The effects of the radial electric fields were less sensitive, whether or not the parabolic velocity profile was considered. In summary, the parabolic velocity profile was significant–especially for charged jets with weak viscosity and strong axial electric intensity. The effects of axial electric fields in the atomization zone, and the effects of fluid permittivity coupled with the axial electric fields, were also investigated here.     

磁拱的运动学无力场

本文首先推导了完全导电流体内运动学磁拱无力场的基本方程，接着考虑了静态解和不定常相似性解．     

由曲率函数和外力场之差支配的凸超曲面的发展

考虑由曲率函数和外力场之差支配的凸超曲面的发展.证明了外力场为常向量场时,初始超曲面的凸性是保持的,且曲率流在有限时间内爆破.对于线性外力场,初始超曲面的凸性保持.而且,若线性常数为负数,则曲率流在有限时间内收敛到一点;若线性常数为正数且初始曲率小于某一与外力场有关的常数,则曲率流光滑地存在于任意有限时间区间,并发散到无穷;若线性常数为正数且初始曲率大于某一与外力场有关的常数,则曲率流在有限时间内爆破.     

Macroscaling Limit Theorems for Filtered Spatiotemporal Random Fields

This article addresses the problem of defining a general scaling setting in which Gaussian and non-Gaussian limit distributions of linear random fields can be obtained. The linear random fields considered are defined by the convolution of a Green kernel, satisfying suitable scaling conditions, with a non-linear transformation of a Gaussian centered homogeneous random field. The results derived cover the weak-dependence and strong-dependence cases for such Gaussian random fields. Extension to more general random initial conditions defined, for example, in terms of non-linear transformations of χ²-random fields, is also discussed. For an example, we consider the random fractional diffusion equation. The vectorial version of the limit theorems derived is also formulated, including the limit distribution of the parabolically rescaled solution to the Burgers equation in the cases of weakly and strongly dependent initial potentials.     

On the Linear Complexity Profile of Nonlinear Congruential Pseudorandom Number Generators with Dickson Polynomials

Linear complexity and linear complexity profile are important characteristics of a sequence for applications in cryptography and Monte-Carlo methods. The nonlinear congruential method is an attractive alternative to the classical linear congruential method for pseudorandom number generation. Recently, a weak lower bound on the linear complexity profile of a general nonlinear congruential pseudorandom number generator was proven by Gutierrez, Shparlinski and the first author. For most nonlinear generators a much stronger lower bound is expected. Here, we obtain a much stronger lower bound on the linear complexity profile of nonlinear congruential pseudorandom number generators with Dickson polynomials.     

On the linear complexity profile of nonlinear congruential pseudorandom number generators with Rédei functions

Linear complexity and linear complexity profile are important characteristics of a sequence for applications in cryptography and quasi-Monte Carlo methods. The nonlinear congruential method is an attractive alternative to the classical linear congruential method for pseudorandom number generation. We prove lower bounds on the linear complexity profile of nonlinear congruential pseudorandom number generators with Rédei functions which are much stronger than bounds known for general nonlinear congruential pseudorandom number generators.     

Debye Sources,Beltrami Fields,and a Complex Structure on Maxwell Fields

The Debye source representation for solutions to the time‐harmonic Maxwell equations is extended to bounded domains with finitely many smooth boundary components. A strong uniqueness result is proved for this representation. Natural complex structures are identified on the vector spaces of time‐harmonic Maxwell fields. It is shown that these complex structures are uniformized by the Debye source representation, that is, represented by a fixed linear map on a fixed vector space, independent of the frequency. This complex structure relates time‐harmonic Maxwell fields to constant‐k Beltrami fields, i.e., solutions of the equation A family of self‐adjoint boundary conditions are defined for the Beltrami operator. This leads to a proof of the existence of zero‐flux, constant‐k, force‐free Beltrami fields for any bounded region in ?³, as well as a constructive method to find them. The family of self‐adjoint boundary value problems defines a new spectral invariant for bounded domains in ?³.© 2015 Wiley Periodicals, Inc.     

Binary Representations of Finite Fields and Their Application to Complexity Theory

Binary representations of finite fields are defined as an injective mapping from a finite field tol-tuples with components in {0, 1} where 0 and 1 are elements of the field itself. This permits one to study the algebraic complexity of a particular binary representation, i.e., the minimum number of additions and multiplications in the field needed to compute the binary representation. The two-way complexity of a binary representation is defined as the sum of the algebraic complexities of the binary representation and of its inverse mapping. Two particular binary representations are studied: the standard representation and the logarithmic representation. A method of surrogate computation is developed and used to deduce relationships between the algebraic complexities of certain functions. The standard representation of a finite field is shown to be among the two-way easiest representations of this field. In particular, the standard representation of a finite field with characteristicpis two-way easy wheneverp− 1 has only small prime factors. For any finite field having a two-way easy binary representation, the algebraic complexity in this field is shown to be essentially equivalent to Boolean circuit complexity. For any finite field, the Boolean circuit complexity of Zech's (or Jacobi's) logarithm is shown to be closely related to the Boolean circuit complexity of the discrete logarithm problem that is used in public-key cryptography.     

MDS Self-Dual Codes over Large Prime Fields

Combinatorial designs have been used widely in the construction of self-dual codes. Recently a new method of constructing self-dual codes was established using orthogonal designs. This method has led to the construction of many new self-dual codes over small finite fields and rings. In this paper, we generalize this method by using generalized orthogonal designs, and we give another new method that creates and solves Diophantine equations over GF(p) in order to find suitable generator matrices for self-dual codes. We show that under the necessary conditions these methods can be applied as well to small and large fields. We apply these two methods to study self-dual codes over GF(31) and GF(37). Using these methods we obtain some new maximum distance separable self-dual codes of small orders.     

Linear complexity profile of binary sequences with small correlation measure

Summary A high linear complexity profile is a desirable feature of sequences used for cryptographical purposes. For a given binary sequence we estimate its linear complexity profile in terms of the correlation measure, which was introduced by Mauduit and Sárk?zy. We apply this result to certain periodic sequences including Legendre sequences, Sidelnikov sequences and other sequences related to the discrete logarithm.     

Volume-preserving Fields and Reeb Fields on 3-manifolds

Volume-preserving field X on a 3-manifold is the one that satisfies LxΩ = 0 for some volume Ω. The Reeb vector field of a contact form is of volume-preserving, but not conversely. On the basis of Geiges-Gonzalo＇s parallelization results, we obtain a volume-preserving sphere, which is a triple of everywhere linearly independent vector fields such that all their linear combinations with constant coefficients are volume-preserving fields. From many aspects, we discuss the distinction between volume-preserving fields and Reeb-like fields. We establish a duality between volume-preserving fields and h-closed 2-forms to understand such distinction. We also give two kinds of non-Reeb-like but volume-preserving vector fields to display such distinction.     

Zak Transforms on Binary Fields

We introduce analogues of the Zak Transform on binary fields, and show that they are bounded linear operators on L^p for p=1 and 2. We also show that positivity of Zak transforms can be used to decide whether orthonormal systems generated by multiplying characters of F by a weight function are complete or not.     

On Conformal Invariants Built from Spinor Fields

By means of a conformal covariant differentiation process we construct generating systems for conformally invariant symmetric (r, s)–spinors in an arbitrary curved space–time. Extending this method to conformally invariant linear differential operators acting on symmetric spinor fields some classes of such operators are derived.