arXiv subjects

Bhupendra Singh

Publications and source records attributed to Bhupendra Singh.

5 recordsLinked to original sources

arXiv2026

On the generalization of $g$-circulant MDS matrices

A matrix $M$ over the finite field $ \mathbb{F}_q $ is called \emph{maximum distance separable} (MDS) if all of its square submatrices are non-singular. These MDS matrices are very important in cryptography and coding theory because they provide strong data protection and help spread information efficiently. In this paper, we introduce a new type of matrix called a \emph{consta-$g$-circulant matrix}, which extends the idea of $g$-circulant matrices. These matrices come from a linear transformation defined by the polynomial $ h(x) = x^m - λ+ \sum_{i=0}^{m-1} h_i x^i $ over $ \mathbb{F}_q $. We find the upper bound of such matrices exist and give conditions to check when they are invertible. This helps us know when they are MDS matrices. If the polynomial $ x^m - λ$ factors as $ x^m - λ= \prod_{i=1}^{t} f_i(x)^{e_i}, $ where each $ f_i(x) $ is irreducible, then the number of invertible consta-$g$-circulant matrices is $ N \cdot \prod_{i=1}^{t} \left( q^{°f_i} - 1 \right), $ where $r$ is the multiplicative order of $λ$, and $ N $ is the number of integers $ k $ such that $ 0 \leq k < \left\lfloor \frac{m - 1}{r} \right\rfloor + 1 \quad \text{and} \quad \gcd(1 + rk, m) = 1. $ This formula help us to reduce the number of cases to check whether such matrices is MDS. Moreover, we give complete characterization of $g$-circulant MDS matrices of order 3 and 4. Additionally, inspired by skew polynomial rings, we construct a new variant of $g$-circulant matrix. In the last, we provide some examples related to our findings.

cs.IT↗

arXiv2026

Malware Classification using Diluted Convolutional Neural Network with Fast Gradient Sign Method

Android malware has become an increasingly critical threat to organizations, society and individuals, posing significant risks to privacy, data security and infrastructure. As malware continues to evolve in terms of complexity and sophistication, the mitigation and detection of these malicious software instances have become more time consuming and challenging particularly due to the requirement of large number of features to identify potential malware. To address these challenges, this research proposes Fast Gradient Sign Method with Diluted Convolutional Neural Network (FGSM DICNN) method for malware classification. DICNN contains diluted convolutions which increases receptive field, enabling the model to capture dispersed malware patterns across long ranges using fewer features without adding parameters. Additionally, the FGSM strategy enhance the accuracy by using one-step perturbations during training that provides more defensive advantage of lower computational cost. This integration helps to manage high classification accuracy while reducing the dependence on extensive feature sets. The proposed FGSM DICNN model attains 99.44% accuracy while outperforming other existing approaches such as Custom Deep Neural Network (DCNN).

cs.CR↗

arXiv2021

Discrete Teissier distribution: properties, estimation and application

In this article, a discrete analogue of continuous Teissier distribution is presented. Its several important distributional characteristics have been derived. The estimation of the unknown parameter has been done using the method of maximum likelihood and the method of moment. Two real data applications have been presented to show the applicability of the proposed model.

stat.ME↗

arXiv2020

A short perspective on the Mascarene High and the abnormal Indian Monsoon during 2015

The initiation of the Indian summer monsoon circulation during late May / early June arises through large-scale land-sea thermal contrast and setting up of negative pressure gradient between the Monsoon Trough over the Indo-Gangetic plains and the Mascarene High over the subtropical Indian Ocean. The meridional pressure gradient together with the Earth's rotation (Coriolis force) creates the summer monsoon cross-equatorial flow, while feedbacks between moisture-laden winds and latent heat release from precipitating systems maintain the monsoon circulation during the June-September (JJAS) rainy season (Krishnamurti and Surgi, 1987). This simplified view of the Indian monsoon is a useful starting point to draw insights into the variability of the large-scale monsoon circulation.

physics.ao-ph↗

arXiv2020

FastV2C-HandNet: Fast Voxel to Coordinate Hand Pose Estimation with 3D Convolutional Neural Networks

Hand pose estimation from monocular depth images has been an important and challenging problem in the Computer Vision community. In this paper, we present a novel approach to estimate 3D hand joint locations from 2D depth images. Unlike most of the previous methods, our model captures the 3D spatial information from a depth image thereby giving it a greater understanding of the input. We voxelize the input depth map to capture the 3D features of the input and perform 3D data augmentations to make our network robust to real-world images. Our network is trained in an end-to-end manner which reduces time and space complexity significantly when compared to other methods. Through extensive experiments, we show that our model outperforms state-of-the-art methods with respect to the time it takes to train and predict 3D hand joint locations. This makes our method more suitable for real-world hand pose estimation scenarios.

cs.CV↗