The Generalized Hamming weights and their relative version, which generalize the minimum distance of a linear code, are relevant to numerous applications, including coding on the wire-tap channel of type II, t-resilient functions, bounding the cardinality of the output in list decoding algorithms, ramp secret sharing schemes, and quantum error correction. The generalized Hamming weights have been determined

The traditional boundary element method (BEM) often faces challenges in efficiently solving inhomogeneous problems, particularly in thin-walled geometries, due to the need for domain discretization and the handling of nearly singular integrals. In this study, we propose an efficient hybrid algorithm that combines the BEM with physics-informed neural networks (PINNs) to solve inhomogeneous potential

Nonlinear feedback shift registers (NFSRs) are widely used in the design of stream ciphers and the cycle structure of an NFSR is a fundamental problem still open. In this paper, a new configuration of Galois NFSRs, called F-Ring NFSRs, is proposed. It is shown that an n-bit F-Ring NFSR generates n sequences with the same period simultaneously, that is, sequences from all bit registers have the same

Numerical simulation of slope instability remains a critical challenge in geotechnical engineering, particularly for large deformations and long-term seepage. The traditional finite element method (FEM) is prone to mesh distortion in large-deformation modeling, while the material point method (MPM) is less efficient for small deformations associated with long-term seepage. To overcome these limitations

This research introduces a dual reciprocity boundary element method (BEM) designed to analyze the transient scattering of vertically travelling incident P-SV waves. By using static fundamental solutions and appropriate predictor operations, the domain inertia integrals from the equilibrium equation were transformed into boundary integral equations. The computable format of the integral equations was

In this work, the ZZ-BD recovered stress field is first used to enhance the data transferred from the global to the local scale models in the Generalized Finite Element Method with Global–Local enrichments (GFEMgl). The recovered stress field is constructed by solving a block-diagonal system of equations resulting from an L2 approximate function projection associated with the singular stress field

The problem of radiation diffusion is extremely challenging due to the complex physical processes and nonlinear characteristics of the equation involved. In this paper, we propose a class of high-precision meshless methods for 3D nonlinear radiation diffusion equations applicable to spherical and cylindrical walls. Firstly, when the energy density is linearly related to temperature, we use a full-implicit

In this study, a new virtual material point peridynamic model (abbreviated as VMPPD) is proposed to capture the fracture behavior of composite laminates with arbitrary fiber orientation. The unique feature is that virtual material points serve as intermediate variables to achieve load transfer in a regularized discrete grid. As a result, a PD model for describing the reinforcement characteristics of

The paper introduces a novel methodology based on a generalized formulation and higher-order-theories for the fully-coupled multifield analysis of laminated curved structures subjected to thermal, magnetic, and mechanical loads. The formulation follows the Equivalent Single Layer approach, taking into account a generalized through-the-thickness expansion of displacement field components, scalar magnetic

Artificial Neural Networks (ANNs) have revolutionized machine learning by enabling systems to learn from data and generalize to new, unseen examples. As biologically inspired models, ANNs consist of interconnected neurons organized in layers, mimicking the human brain’s functioning. Their ability to model complex, nonlinear processes makes them powerful tools in various domains. In this study, the

Nonlinear feedback shift registers (NFSRs) are used in many recent stream ciphers as their main building blocks. Two NFSRs are said to be isomorphic if their state diagrams are isomorphic, and to be equivalent if their sets of output sequences are equal. So far, numerous work has been done on the equivalence of NFSRs with same bit number, but much less has been done on their isomorphism. Actually,

A De Bruijn cycle is a cyclic sequence in which every word of length n over an alphabet \(\mathcal {A}\) appears exactly once. De Bruijn tori are a two-dimensional analogue. Motivated by recent progress on universal partial cycles and words, which shorten De Bruijn cycles using a wildcard character, we introduce universal partial tori and matrices. We find them computationally and construct infinitely

Traditional model for composite laminae based on bond-based peridynamics (BB-PD) involves only two material parameters, which is insufficient to fully describe the complicated engineering properties of composite laminae. This limitation results in constrained Poisson's ratio and shear modulus in the PD model. In this study, a novel fracture model for composite laminae is proposed based on BB-PD, which

The generalized nth-order perturbation method for the quantitative uncertainty analysis in half-space acoustic problems proposed in this study is based on the isogeometric boundary element method, where the acoustic wave frequency is defined as a stochastic variable. We derive the Taylor series expansion and the kernel function formulation of the acoustic boundary integral equation for the half-space

Numerical solutions of initial value problems (IVPs) for stiff differential equations via explicit methods such as Euler’s method, trapezoidal method and Runge–Kutta methods suffer from stability issues and demand unacceptably small time steps. Backward differentiation formulas (BDF), a class of implicit methods, have been successfully used for resolving stiff IVPs. Classical BDF methods are derived

Fracture initiation in solids fundamentally arises from pre-existing discontinuities, such as crack networks and void distributions, which are ubiquitously observed in engineering structures. This paper presents an innovative unsupervised learning framework, termed Kolmogorov–Arnold representation theorem enhanced peridynamic-informed neural network (PD-KINN), designed to address challenges in elastic

The Mechatronic Electro-Hydraulic Coupler (MEHC) integrates a swashplate axial piston pump with a permanent magnet synchronous motor, enabling flexible conversion between mechanical, electrical, and hydraulic energy. The efficiency of the MEHC plays a crucial role in the selection of loading and control strategy. However, specific research on its hydraulic energy loss is lacking. This paper proposes

In this paper, for an odd prime power q and an integer \(m\ge 2\), let \(\mathcal {C}(q,m)\) be a one-weight irreducible cyclic code with parameters \([q^m-1,m,(q-1)q^{m-1}]\), we consider the complete weight enumerator and the weight distribution of the square \(\big (\mathcal {C}(q,m)\big )^2\), whose dual has \(\lfloor \frac{m}{2}\rfloor +1\) zeros. Using the character sums method and the known

The learning parity with noise (LPN) problem underlines several classic cryptographic primitives. Researchers have attempted to show the algorithmic difficulty of this problem by finding a reduction from the decoding problem of linear codes, for which several hardness results exist. Earlier studies used code smoothing as a technical tool to achieve such reductions for codes with vanishing rate. This

Detailed studies of peculiar wave phenomena in piezoelectric metamaterials require advanced and accurate numerical methods. An extended boundary integral equation method based on the employment of the Fourier transform of Green’s matrices and the Bubnov–Galerkin method is presented for the wave motion simulation of a multi-layered piezoelectric laminate with electrode arrays connected pairwise via

In this paper, we introduce and study the problem of binary stretch embedding of edge-weighted graphs in both integer and fractional settings. Roughly speaking, the binary stretch embedding problem for a weighted graph G is to find a mapping from the vertex set of G, to the vertices of a hypercube graph such that the distance between every pair of the vertices is not reduced under the mapping, hence

In this paper, we consider the numerical solutions of three-dimensional axisymmetric nonlinear boundary integral equations with logarithmic kernel. A numerical algorithm with using extrapolation twice is developed to solve the equations, which possesses the low computing complexities and high accuracy. The asymptotic compact operator theory is used to prove the convergence of the algorithm. The efficiency

Understanding the Site-City Interaction (SCI) induced by surface wave is vital for accurate seismic analysis and urban planning. Based on the elastodynamics theory and wave equations, this paper proposes a semi-analytical method to investigate SCI effect induced by Rayleigh wave. The proposed approach integrates the Dynamic Stiffness Matrix Method (DSMM) with substructure method, and can effectively

This study introduces an online reduced-order methodology designed to avoid the need for generating additional samples during the offline phase, a requirement typically associated with the classical reduced basis method. The proposed methodology is implemented for accelerating the sensitivity analysis in the dynamic topology optimization. The dominant Proper Orthogonal Mode (POM) of the adjoint sensitivity

A \(2-(v, k, \lambda )\) design is additive if, up to isomorphism, the point set is a subset of an abelian group G and every block is zero-sum. This definition was introduced in Caggegi et al. (J Algebr Comb 45:271-294, 2017) and was the starting point of an interesting new theory. Although many additive designs have been constructed and known designs have been shown to be additive, these structures

A novel fully nonlinear circular numerical wave basin is developed based on potential flow theory and high-order boundary element methods (HOBEM). By controlling the vector input of wave velocity from wave-making sources uniformly distributed on the three-dimensional cylindrical surface, the wave basin is capable of generating waves in all directions. The wave basin is used to simulate nonlinear waves

The combined effect of dual rigid structures over non-periodic bottom morphologies is examined through a boundary value problem to characterize the scattering phenomenon. Three different types of bottom morphologies: (a) monotonically decreasing oscillatory, (b) exponential decreasing oscillatory and (c) Gaussian oscillatory are taken into consideration. Utilizing the boundary element method (BEM)

Lattices have many significant applications in cryptography. In 2021, the p-adic signature scheme and public-key encryption cryptosystem were introduced. They are based on the Longest Vector Problem (LVP) and the Closest Vector Problem (CVP) in p-adic lattices. These problems are considered to be challenging and there are no known deterministic polynomial time algorithms to solve them. In this paper

This study considers transient response of sandwich beams produced from functionally graded graphene platelets-reinforced composite faces and functionally graded porous core under the action of various types of moving distributed masses. The equations of motion are developed by the energy method using a von Kármán type nonlinear strain-displacement relationship. Different micromechanical models are

Earthquakes can occur onshore and offshore. When it occurs offshore, an analytical model is needed where both the water layers and rock layers have to be considered. In this paper, we develop such a new solution when a general dislocation source is located in any layer of the transversely isotropic and elastic rock media. This novel and comprehensive method is based on the Fourier-Bessel series system

Homomorphic encryption (HE) is one of the mainstream cryptographic tools used to enable secure outsourced computation. A typical task is secure matrix computation, which is a fundamental operation used in various outsourced computing applications such as statistical analysis and machine learning. In this paper, we present a new framework for secure multiplication of two matrices with size \(r \times

Boundary element methods for elliptic partial differential equations typically lead to boundary integral operators with translation-invariant kernel functions. Taking advantage of this property is not straightforward if general unstructured meshes and general basis functions are used, since we need the supports of these basis functions to be contained in a hierarchy of subdomains with translational

A function \(f: {\mathbb {F}}_q \rightarrow {\mathbb {F}}_q\), is called an almost perfect nonlinear (APN) if \(f(X+a)-f(X) =b\) has at most 2 solutions for every \(b,a \in {\mathbb {F}}_q\), with a nonzero. Furthermore, it is called an exceptional APN if it is an APN on infinitely many extensions of \({\mathbb {F}}_q\). These problems are equivalent to finding rational points on the corresponding

Impossible differential cryptanalysis is a crucial cryptanalytical method for symmetric ciphers. Given an impossible differential, the key recovery attack typically proceeds in two steps: generating pairs of data and then identifying wrong keys using the guess-and-filtering method. At CRYPTO 2023, Boura et al. first proposed a new key recovery technique—the differential meet-in-the-middle attack, which

A problem of current interest, also motivated by applications to Coding theory, is to find explicit equations for maximal curves, that are projective, geometrically irreducible, non-singular curves defined over a finite field \(\mathbb {F}_{q^2}\) whose number of \(\mathbb {F}_{q^2}\)-rational points attains the Hasse-Weil upper bound \(q^2+2\mathfrak {g}q+1\) where \(\mathfrak {g}\) is the genus of

Multiphase flow simulations are complex due to the intricate interactions between phases when high density and viscosity ratios are involved. These complexities often lead to challenges in capturing sharp interfaces and managing pressure jumps across phases, which can induce numerical instability. Extending the Lagrangian Differencing Dynamics (LDD) method which differs from other meshless methods

Dynamic response of a transversely isotropic layered half-space composed of alternatively arbitrary poroelastic and elastic materials is numerically investigated through the Meshless Local Petrov–Galerkin (MLPG) method. The governing equations of the porous layers are the u−p formulation of the Biot’s theory, and the equations of motion for single-phase elastic media are considered for pure elastic

The blast threats have become a global safety concern for the ecosystems. Rigorous research using blasts over infrastructures improves the assessment methods, damages and failure modes, either experimentally or numerically. However, experimental blast analysis over a full-scale bridge is not feasible and is against the country's federal law. Alternatively, numerical analysis with experimentally validated

In this study, we derived a three-dimensional scaled boundary finite element formulation for heat conduction problems. By incorporating Wachspress shape functions, a polyhedral scaled boundary finite element method (PSBFEM) was proposed to address heat conduction challenges in complex geometries. To address the complexity of traditional methods, this work introduced polygonal discretization techniques

Tunnel engineering is one of the hot spots of research in the field of geotechnical engineering, and the seepage analysis of tunnels is an important research direction at present. In recent years, physics-informed deep learning based on priori fusion data has become a cross-disciplinary hotspot for solving forward and inverse problems based on partial differential equations (PDEs). In this paper, physics-informed

It has recently been demonstrated that turbulent flow could be described by the fractional Laplacian Reynolds-averaged Navier–Stokes equations fL-RANS equations, (Epps and Cushman-Roisin, 2018). In this paper, we propose a numerical approach for solving the equations, and then provide a deep-learning based approach for inferring the unknown parameters of the equations. First, we construct a lattice

Multivariate public key cryptography (MPKC) is one of the most promising alternatives to build quantum-resistant signature schemes, as evidenced in NIST’s call for additional post-quantum signature schemes. The main assumption in MPKC is the hardness of the Multivariate Quadratic (MQ) problem, which seeks for a common root to a system of quadratic polynomials over a finite field. Although the Crossbred

The study presents an adapted MeshGraphNet for real-time field prediction in digital twins, surpassing traditional FEM in efficiency and boundary condition adaptability but falling short of real-time computational demands. Trained with true labels, MeshGraphNet accurately predicts nodal variables on coarse graphs and reduces simulation time through parallel sub-mesh processing. Applied to a 1D mesh

An efficient numerical integration technique, namely the Element Midpoint(EM) Method, is successfully applied to meshless methods to solve the fracture problem, which is modeled using the Radial point interpolation method. The results were compared with standard (3×3) points Gauss quadrature and (6×6) points Gauss quadrature in 2D to validate the presented numerical methods. To demonstrate the efficiency

The Internet of Things (IoT) has become a necessary part of modern technology, enabling devices to connect and interact with each other. Unless applicable cryptographic components have adequate security protection, the IoT could easily leak private data. Impossible differential cryptanalysis (IDC) is one of the best-known techniques for cryptanalysis of block ciphers. Several papers are aimed at formalizing

Discontinuous numerical methods have been widely applied to investigate rock deformation and failure behavior in rock engineering scenarios such as tunnel excavation and oil/gas exploitation. Compared to discontinuous numerical methods with explicit formulations, discontinuous deformation analysis (DDA) has the advantages of unconditional stability and strict contact convergence with its implicit formulation

We present a new result on the nonexistence of generalized bent functions (GBFs) from \((\mathbb {Z}/t\mathbb {Z})^n\) to \(\mathbb {Z}/t\mathbb {Z}\) (called type [n, t]) for a large class. Assume p is an odd prime number. By showing certain quadratic norm form equations having no integral points, we obtain a universal result on the nonexistence of GBFs with type \([n, 2p^e]\) when p and n satisfy

In large-scale water diversion projects, the rapid and accurate evaluation of pumping station unit performance is crucial to ensure that flow rates meet delivery requirements. Computational fluid dynamics (CFD) is effective in analyzing unit performance but is constrained by its high computational complexity and time consumption. Reduced-order models (ROMs) partially alleviate these issues; however

In the study of the stability of gravity dam, the situation of dam and rock mass is complicated, there may be pore water and various kinds of heterogeneous materials to affect the stability of rock mass, among which the deformation and failure of the dam cannot be ignored. In this paper, an improved high-order covering function is applied to the Numerical Manifold Method (NMM), and the Hermite form

This paper provides new bounds on the size of spheres in any coordinate-additive metric with a particular focus on improving existing bounds in the sum-rank metric. We derive improved upper and lower bounds based on the entropy of a distribution related to the Boltzmann distribution, which work for any coordinate-additive metric. Additionally, we derive new closed-form upper and lower bounds specifically

Let \(\ell ^m\) be a power with \(\ell \) a prime greater than 3 and \(m\) a positive integer such that 3 is a primitive root modulo \(2\ell ^m\). Let \(\mathbb {F}_3\) be the finite field of order 3, and let \(\mathbb {F}\) be the \(\ell ^{m-1}(\ell -1)\)-th extension field of \(\mathbb {F}_3\). Denote by \(\text {Tr}\) the absolute trace map from \(\mathbb {F}\) to \(\mathbb {F}_3\). For any \(\alpha

We study the hardness of the Syndrome Decoding problem, the base of most code-based cryptographic schemes, such as Classic McEliece, in the presence of side-channel information. We use ChipWhisperer equipment to perform a template attack on Classic McEliece running on an ARM Cortex-M4, and accurately classify the Hamming weights of consecutive 32-bit blocks of the secret error vector \(\textbf{e}\in

We compute the weight distribution of the binary Reed–Muller code \({\mathcal {R}} (4,9)\) by combining the methodology described in D. V. Sarwate’s Ph.D. thesis from 1973 with newer results on the affine equivalence classification of Boolean functions. More specifically, to address this problem posed, e.g., in the book of MacWilliams and Sloane, we apply an enhanced approach based on the classification

Given two linear codes, the code equivalence problem asks to find an isometry mapping one code into the other. The problem can be described in terms of group actions and, as such, finds a natural application in signatures derived from a Zero-Knowledge Proof system. A recent paper, presented at Asiacrypt 2023, showed how a proof of equivalence can be significantly compressed by describing how the isometry

Due to the many applications of shape memory alloys (SMAs) to make the structures more intelligent, these materials are getting great attention of researchers. Meanwhile, the nonlinear dynamic analysis of curved beams made of SMAs has not been investigated so far. Therefore, this work focuses on a nonlinear dynamic analysis of SMA curved beams under transverse impulse loading taking into account the

We introduce a novel semi-analytic method for solving singularly perturbed reaction–diffusion problems in a smooth domain using neural network architectures. To manage steep solution transitions near the boundary, we utilize the boundary-fitted coordinates and perform boundary layer analysis to construct a corrector function which describes the singular behavior of the solution near the boundary. By

A novel computational framework based on modified bond-based peridynamics is proposed for viscoelastic laminas. The framework accurately captures deformations, damage initiation, and propagation under mechanical and thermal loads. It reduces numerical complexity by directly assessing viscoelastic strains each time step, eliminating real-time increment constraints. Constitutive component models, including

We consider various method of fundamental solution (MFS) formulations for the numerical solution of two-dimensional boundary value problems (BVPs) governed by the homogeneous biharmonic equation. The motivation for employing the proposed techniques comes from the corresponding boundary integral representations. These are carefully analyzed in the case the domain of the BVP under consideration is a

This paper focuses on the study of triple-twisted generalized Reed–Solomon (TTGRS) codes over a finite field \({\mathbb {F}}_q\), having twists \(\varvec{t} = (1, 2, 3)\) and hooks \(\varvec{h} = (0, 1, 2)\). We have obtained the necessary and sufficient conditions for such TTGRS codes to be MDS, AMDS, and AAMDS via algebraic techniques. We have also enumerated these codes for some particular values