Cyclic codes are a subclass of linear codes and have wide applications in data storage systems, communication systems and consumer electronics due to their efficient encoding and decoding algorithms. Let \(\alpha \) be a generator of \(\mathbb F_{3^m}\setminus \{0\}\), where m is a positive integer. Denote by \(\mathcal {C}_{(i_1,i_2,\cdots , i_t)}\) the cyclic code with generator polynomial \(m_{\alpha

In this paper, we promote Trojan message attacks against Merkle–Damgård hash functions and their concatenation combiner in quantum settings for the first time. Two main quantum scenarios are considered, involving the scenarios where a substantial amount of cheap quantum random access memory (qRAM) is available and where qRAM is limited and expensive to access. We first discuss the construction of diamond

In the present article, the research work of many years is summarized in an interim report. This concerns the connection between logic, space, time and matter. The author always had in mind two things, namely 1. The discovery/construction of an interface between matter and mind, and 2. some entry points for the topos view that concern graphs, grade rotations and contravariant involutions in geometric

Combinatorial neural (CN) codes are binary codes introduced firstly by Curto et al. for asymmetric channel, and then are further studied by Cotardo and Ravagnani under the metric \(\delta _r\) (called asymmetric discrepancy) which measures the differentiation of codewords in CN codes. When \(r>1\), CN codes are different from the usual error-correcting codes in symmetric channel (\(r=1\)). In this

We study the complexity of the Code Equivalence Problem on linear error-correcting codes by relating its variants to isomorphism problems on other discrete structures—graphs, lattices, and matroids. Our main results are a fine-grained reduction from the Graph Isomorphism Problem to the Linear Code Equivalence Problem over any field \(\mathbb {F}\), and a reduction from the Linear Code Equivalence Problem

Projective Reed–Muller codes are constructed from the family of projective hypersurfaces of a fixed degree over a finite field \(\mathbb {F}_q\). We consider the relationship between projective Reed–Muller codes and their duals. We determine when these codes are self-dual, when they are self-orthogonal, and when they are LCD. We then show that when q is sufficiently large, the dimension of the hull

Accurate modeling of basin structures and quantitative analysis of basin amplification effects are critical for seismologists and engineers. The Indirect Boundary Element Method (IBEM), developed from the Boundary Element Method (BEM), is particularly well-suited for these tasks due to its capability to manage layers with lateral inhomogeneities. However, current IBEM studies mostly focus on wavefields

The study of complex functions is based around the study of holomorphic functions, satisfying the Cauchy-Riemann equations. The relatively recent field of Clifford Analysis lets us extend many results from Complex Analysis to higher dimensions. In this paper, I decompose the Cauchy-Riemann equations for a general Clifford algebra into grades using the Geometric Algebra formalism, and show that for

A two-dimensional time domain coupled model is developed to analyze the interaction between fully nonlinear waves and floating bodies over variable topography. The whole calculation domain is divided into an inner domain close to the structure and two outer domains far away from the structure. The fully nonlinear free surface boundary conditions are used in each sub-domain. Irrotational Green-Naghdi

This work presents a new and robust formulation for studying the effect of point heat sources on three-dimensional thermomechanical contact problems. The aim of this work is to accurately analyze heat dissipation in microchips with known heat sources. To achieve this, the Boundary Element Method (BEM) has been used to calculate the thermomechanical influence coefficients. The traditional BEM has been

This study presents a novel volume compensation model for multi-resolution moving particle method simulating free surface flows. The volume-compensation model is developed to conserve volume when simulating free surface flow using multi-resolution particles, a topic that has been rarely discussed for multi-resolution simulations in previous literature. The free surface is reconstructed by a linear

The characterization and understanding of cracking propagation behaviors in non-uniform geological structures are crucial for predicting the mechanical response of rock-like materials under varying loading conditions. In this study, an improved Peridynamics (PD) model with degree of heterogeneity characterized by random pre-breaking "bond" ratio is introduced to capture the intricacies of crack initiation

Although kernel functions play a pivotal role in meshfree approximation, the selection of kernel functions is often experience-based and lacks a theoretical basis. As an attempt to resolve this issue, a rational matching between kernel functions and nodal supports is proposed in this work for Galerkin meshfree methods, where the quadratic through quintic B-spline kernel functions are particularly investigated

In this paper, we propose a numerical formula to calculate time-harmonic electromagnetic field interacting with three-dimensional elastic body. The formula is based on the method of fundamental solutions. Firstly, we perform Helmholtz decomposition on the displacement field. The problem will transform into a coupled bounded problem including a scaler Helmholtz equation, a vector Helmholtz equation

In this paper, a series of novel sphere elements are proposed in the boundary element method (BEM). These elements are designed as isoparametric closure elements to simulate spherical geometries with greater accuracy and fewer nodes than conventional boundary elements. Constructed similarly to multi-dimensional Lagrange elements, these sphere elements utilize trigonometric bases for each dimension

Using codes defined over \(\mathbb {F}_4\) and \(\mathbb {F}_2 \times \mathbb {F}_2\), we simultaneously define the theta series of corresponding lattices for both real and imaginary quadratic fields \(\mathbb {Q}(\sqrt{d})\) with \(d \equiv 1\mod 4\) a square-free integer. For such a code, we use its weight enumerator to prove which term in the code’s corresponding theta series is the first to depend

Cyclic codes, as a special type of constacyclic codes, have been extensively studied due to their favorable theoretical and mathematical properties. Very recently, by using the derivative of the Mattson-Solomon polynomials, Huang and Zhang (IEEE Trans Inf Theor 70(4):2395–2410, 2024) studied the cyclic derivative descendants (DDs) and linear DDs of binary extended cyclic codes and proposed the corresponding

A bijection \(\theta :G\rightarrow G\) of a finite group G is an orthomorphism of G if the mapping \(x\mapsto x^{-1}\theta (x)\) is also a bijection. Two orthomorphisms \(\theta \) and \(\phi \) of a finite group G are orthogonal if the mapping \(x\mapsto \theta (x)^{-1}\phi (x)\) is also bijective. We show that there is a pair of orthogonal orthomorphisms of a finite nilpotent group G if and only

Brawley and Carlitz introduced diamond products of elements of finite fields and associated composed products of polynomials in 1987. Composed products yield a method to construct irreducible polynomials of large composite degrees from irreducible polynomials of lower degrees. We show that the composed product of two irreducible polynomials of degrees m and n is again irreducible if and only if m and

In this paper we demonstrate the first example of a finite translation plane which does not contain a translation hyperoval, disproving a conjecture of Cherowitzo. The counterexample is a semifield plane, specifically a Generalised Twisted Field plane, of order 64. We also relate this non-existence to the covering radius of two associated rank-metric codes, and the non-existence of scattered subspaces

In this work we present results on the classification of \(\mathbb {F}_{q^n}\)-linear MRD codes of dimension three. In particular, using connections with certain algebraic varieties over finite fields, we provide non-existence results for MRD codes \(\mathcal {C}=\langle X^{q^t}, F(X), G(X) \rangle \subseteq \mathcal {L}_{n,q}\) of exceptional type, i.e. such that \(\mathcal {C}\) is MRD over infinitely

Set systems with strongly restricted intersections, called \(\alpha \)-intersecting families for a vector \(\alpha \), were introduced recently as a generalization of several well-studied intersecting families including the classical oddtown and eventown. Given a binary vector \(\alpha =(a_1, \ldots , a_k)\), a collection \({\mathcal {F}}\) of subsets over an n element set is an \(\alpha \)-intersecting

In this paper, a novel spatial-temporal collocation solver is proposed for the solution of 2D and 3D long-time diffusion problems with source terms varying over time. In the present collocation solver, a series of semi-analytical spatial-temporal fundamental solutions are used to approximate the solutions of the time-dependent diffusion equations with only the node discretization of the initial and

The submarine's sail, as the largest appendage structure, is more susceptible to turbulence induced vibrations during medium to high-speed navigation, making it a critical area for the generation of flow-induced noise, significantly impacting the stealth and safety of submarine. Considering the excellent mechanical properties and high damping characteristics of lightweight composite sandwich structures

This study is concerned with rigid-body responses and elastic motion of floating offshore wind turbines (FOWTs) under combined wave, current and wind loads. A numerical approach is developed in frequency domain based on the linear diffraction theory with a Green function for small current speeds and the blade-element momentum method for hydrodynamic and aerodynamic analysis, respectively. This approach

Nanostructures play a vast role in the current Internet of NanoThings (IoNT) era due to remarkable properties and features that precisely impart their desired application functions in catalysis, energy and other fields. The exploration in understanding their minute features caused by the flexibility of compositional and complex atomic arrangement from the synthesis reaction widely opens for the in-depth

In this paper, we apply the semi-tensor product of matrices and the real vector representation of a quaternion matrix to find the least squares lower (upper) triangular Toeplitz solution of \(AX-XB=C\), \(AXB-CX^{T}D=E\) and (anti)centrosymmetric solution of \(AXB-CYD=E\). And the expressions of the least squares lower (upper) triangular Toeplitz and (anti)centrosymmetric solution for the studied equations

Ice-water coupling is a unique fluid-solid interaction problem characterized by collisions and hydrodynamic interaction between multiple bodies, accompanied by significant changes in the free surface. This paper presents a novel numerical model that achieves two-way coupling between the moving particle semi-implicit (MPS) method and the non-smooth discrete element method (NDEM) to simulate ice-water

Piezoelectric materials are extensively used in engineering for the fabrication of sensors, transducers, and actuators. Due to the coupling characteristics, anisotropy, and arbitrariness of polarization directions, the tasks of mesh generation, numerical integration, and global equation formulation involved in numerical computations are complex and nontrivial. To solve electrostatic and electroelastic

In recent years, Physics-Informed Neural Networks (PINN) have emerged as powerful meshless numerical methods for solving partial differential equations (PDEs) in engineering and science, including the field of structural vibration. However, PINN struggles due to the spectral bias when the target PDEs exhibit high-frequency features. In this work, a meshless Runge-Kutta-based PINN (R-KPINN) framework

This study focuses on the numerical simulation of bubble growth in microchannels and addresses the interfacial deformations associated with phase transitions in the Volume of Fluid (VOF) method. In order to avoid the blurred deformation of the interface during bubble growth, a gradient-constrained algorithm is proposed to simulate bubble growth with sharp interface. The algorithm proposed in this paper

This paper introduces an efficient hybrid numerical discretization method designed to address the coupled mechanical challenges of geomechanics and fluid flow during pressure depletion in tight reservoirs. Utilizing the extended finite element method, this approach solves the elastic deformation of rock, while the mixed boundary element method precisely calculates the unsteady fluid exchange between

Recently, deep learning has been tried to improve the efficiency of compressed ghost imaging. However, these current learning-based ghost imaging methods have to modify and retrain the learning model to cope with different sampling ratios. This will consume a lot of computing resources and energy. In this paper, we propose a deep learning-based compressed ghost imaging method that can adapt to arbitrary

An accurate and stable weighted-least-squares multi-physical particle-based (WLS-MPP) hybrid model is developed to simulate the incompressible generalized Newtonian two-phase magnetohydrodynamics (MHD) flows, and then it is extended to predict a bubble rising process in shear-thinning MHD flow with large density difference, for the first time. The development of WLS-MPP hybrid model for two-phase MHD

This paper develops an improved weakly compressible smoothed particle hydrodynamics (SPH) method for simulating multiphase flows with complex interface and large density ratios. Surface tension is computed using a continuum surface force method along with a kernel gradient correction algorithm, thereby improving the numerical precision of normal vectors and curvatures. To maintain a uniform particle

An infinite-dimensional family of exact solutions of a three-dimensional biharmonic equation was constructed by the hypercomplex method.

In this paper, we investigate the eigenvalues of quaternion tensors under Einstein Product and their applications in color video processing. We present the Ger\(\check{s}\)gorin theorem for quaternion tensors. Furthermore, we have executed some experiments to validate the efficacy of our proposed theoretical framework and algorithms. Finally, we contemplate the application of this methodology in color

In recent years, it has become a popular trend to propose quantum versions of classical attacks. The rectangle attack as a differential attack is widely used in symmetric cryptanalysis and applied on many block ciphers. To improve its efficiency, we propose a new quantum rectangle attack firstly. In rectangle attack, it counts the number of valid quartets for each guessed subkeys and filters out subkey

To explore the rockburst proneness of rock materials, coarse-grained granite, red sandstone and white marble were selected for uniaxial compression laboratory tests. Applying the rockburst proneness criterion based on the peak strength strain storage index, numerical models of the three rocks were constructed according to the three-dimensional Clump (3D-Clump) modelling method using the three-dimensional

In this study, a Hybrid Spectral Element Method (HSEM) integrated with Equivalent Static Load (ESL) in the frequency domain is suggested. This integration aims to enhance the computational efficiency of dynamic topology optimization. In comparison with existing techniques, the proposed HSEM transforms the governing equation of dynamic analysis into a spectral element equation within the frequency domain

In the research of explosion shock theory and engineering application, the convergence of detonation waves can be realized by using multiple initiation points to utilize the detonation energy and pressure effectively. To study the propagation process of detonation wave and the distribution law of impact energy of the explosive with multiple initiation points, a detonation calculation model of the explosive

Grouting is a widely used technique in underground engineering by enhancing mechanical properties of jointed rock mass. Understanding the shear characteristics of jointed coal mass after grouting reinforcement is crucial for optimizing grouting parameters and advancing grouting mechanism. This study proposed a grout-filled jointed coal (GJC) direct shear discrete element model (GJCS-DEM). The model

Achieving tight security is a fundamental task in cryptography. While one of the most important purposes of this task is to improve the overall efficiency of a construction (by allowing smaller security parameters), many current lattice-based instantiations do not completely achieve the goal. Particularly, a super-polynomial modulus seems to be necessary in all prior work for (almost) tight schemes

Floating ice can be damaged by the bubble loads generated by releasing high-pressure gas underwater using an air-gun, so ice-breaking by underwater high-pressure bubble loads is becoming one of the effective ice-breaking technologies. A numerical model was established to study the motion and damage of floating ice subjected to high-pressure bubble loads. Empirical formulas were used to calculate the

In this paper, formulations for asymptotic homogenization method based on the boundary element method (BEM) are presented for the estimations for effective parameters of unidirectional fiber reinforced composites in the 2D plane strain case. The boundaries are discretized by shape functions of non-uniform rational B-splines (NURBS) according to the features of isogeometric analysis and the related

The problem of concentrating electromagnetic fields into a nanotube from an ambient source of light, is considered. An isogeometric analysis approach, in a boundary element method setting, is employed to evaluate the local electric field, which is represented with the exact same basis functions used in the geometric representation of the nanotube. Subsequently, shape optimization of the nanotubes is

A novel fundamental solution based finite element method (HFS-FEM) is proposed to analyze heat conduction problem of two-dimensional composite materials. In the proposed method, a linear combination of fundamental solutions at source points is taken as intra-element trial functions to construct the interior temperature field. The required fundamental solution is established by the charge simulation

The Brakerski–Gentry–Vaikuntanathan (BGV) scheme is a Fully Homomorphic Encryption (FHE) cryptosystem based on the Ring Learning With Error (RLWE) problem. Ciphertexts in this scheme contain an error term that grows with operations and causes decryption failure when it surpasses a certain threshold. Consequently, the parameters of BGV need to be estimated carefully, with a trade-off between security

We compute and explore the full geometric product of two oriented points in conformal geometric algebra Cl(4, 1) of three-dimensional Euclidean space. We comment on the symmetry of the various components, and state for all expressions also a representation in terms of point pair center and radius vectors.

In this paper, we improve the traditional space-time radial basis function (RBF) collocation method for solving three-dimensional elastodynamic problems. The proposed approach arranges source points outside the entire space-time domain by introducing space and time amplification factors, rather than locating them within the computational domain. Additionally, a multiple-scale technique is developed

A generalization of a recently introduced recursive numerical method (Gumerov et al., 2023) for the exact evaluation of integrals of regular solid harmonics and their normal derivatives over simplex elements in R3 is presented. The original Quadrature to Expansion (Q2X) method (Gumerov et al., 2023) achieves optimal per-element asymptotic complexity for computing O(ps2) integrals of all regular solid

This paper presents a fluid topology optimization method utilizing a quadtree scaled boundary finite element method (SBFEM). The method aims to minimize energy dissipation during fluid flow by employing quadtree mesh refinement in the design domain, integrating both velocity and pressure fields. Finer meshes are used near the fluid-structure interface and coarser meshes elsewhere. By leveraging the

It is important to study the new construction methods of bent functions. In this paper, we first propose a secondary construction method of \((k+s)\)-variable bent function g through a family of s-plateaued functions \(f_0,f_1,\ldots ,f_{2^s-1}\) on k variables with disjoint Walsh supports, which can be obtained through any given \((k-s)\)-variable bent function f by selecting \(2^s\) disjoint affine

We are dedicated to addressing Riemann–Hilbert boundary value problems (RHBVPs) with variable coefficients, where the solutions are valued in the Clifford algebra of \(\mathbb {R}_{0,n}\), for biaxially monogenic functions defined in the biaxially symmetric domains of the Euclidean space \(\mathbb {R}^{n}\). Our research establishes the equivalence between RHBVPs for biaxially monogenic functions defined

Defect identification is an important issue in structural health monitoring. Herein, originated from inverse techniques, a merging approach is established by the numerical manifold method (NMM) and whale optimization algorithm-back propagation (WOA-BP) cooperative neural network to identify hole defects in heat conduction problems. On the one hand, the NMM can simulate varying hole configurations on

We consider the problem of approximating a linear differential operator on several specific stencils using the radial basis function method in the finite difference scheme. We prove a linear convergence order on a non-equispaced five-point stencil. Then, we discuss how the convergence rate can be boosted up to the second-order on an equispaced stencil. Moreover, we show that including additional nearby

In this article, a new high-order, local meshless technique is presented for numerically solving multi-dimensional Sobolev equation arising from fluid dynamics. In the proposed method, Hermite radial basis function (RBF) interpolation technique is applied to approximate the operators of the model over local stencils. This leads to compact RBF generated finite difference (RBF-FD) formula, which provides

The development of new numerical methods for fluid flow simulations is challenging but such tools may help to understand flow problems better. Here, the Boundary-Domain Integral Method is applied to simulate laminar fluid flow governed by a dimensionless velocity–vorticity formulation of the Navier–Stokes equation. The Reynolds number is chosen in all examples small enough to ensure laminar flow conditions

Let n be an odd positive integer, p be an odd prime with \(p\equiv 3\pmod 4\), \(d_{1} = {{p^{n}-1}\over {2}} -1 \) and \(d_{2} =p^{n}-2\). The function defined by \(f_u(x)=ux^{d_{1}}+x^{d_{2}}\) is called the generalized Ness–Helleseth function over \(\mathbb {F}_{p^n}\), where \(u\in \mathbb {F}_{p^n}\). It was initially studied by Ness and Helleseth in the ternary case. In this paper, for \(p^n

The community has been pursuing improvements in the cardinalities for constant dimensional codes (CDC for short) for the past decade. Lao et al. (IEEE Trans Inf Theory 69(7):4333–4344, 2023) has shown that mixed dimension subspace codes can be used to construct large constant dimension subspace codes. The exploration of the CDCs’ construction is transformed into finding mixed dimension/distance subspace