Searcharxiv⌕ Search

arXiv subjects

R. K. Sharma

Publications and source records attributed to R. K. Sharma.

At least 19 recordsLinked to original sources
arXiv2025

Construction of Additive Complementary Dual Codes Over Finite Fields

In this work, we investigate additive complementary dual (ACD) codes and their construction over finite fields $\mathbb{F}_{q^2}$ with respect to the trace inner products, where $q$ is a prime power. First, we associate an additive code with a matrix known as a generator matrix. After that, we describe ACD codes in terms of generator matrices for the trace Hermitian and the trace Euclidean inner products. We also construct ACD codes over $\mathbb{F}_{q^2}$ from linear codes over $\mathbb{F}_q.$ Additionally, we present techniques for constructing ACD codes with various parameters from a given ACD code over $\mathbb{F}_{q^2}.$ By applying these methods, we construct numbers of trace Euclidean and trace Hermitian ACD codes that exhibit better parameters compared to the best known linear codes over $\mathbb{F}_9$ and $\mathbb{F}_4$ of the same size and length.

cs.IT↗
arXiv2025

$r$-primitive $k$-normal polynomials over finite fields with last two coefficients prescribed

Let $ξ\in\mathbb{F}_{q^m}$ be an $r$-primitive $k$-normal element over $\mathbb{F}_q$, where $q$ is a prime power and $m$ is a positive integer. The minimal polynomial of $ξ$ is referred to be the $r$-primitive $k$-normal polynomial of $ξ$ over $\mathbb{F}_q$. In this article, we study the existence of an $r$-primitive $k$-normal polynomial over $\mathbb{F}_q$ such that the last two coefficients are prescribed. In this context, first, we prove a sufficient condition which guarantees the existence of such a polynomial. Further, we compute all possible exceptional pairs $(q,m)$ in case of $3$-primitive $1$-normal polynomials for $m\geq 7$.

math.NT↗
arXiv2025

Enhancing Robustness and Efficiency of Least Square Twin SVM via Granular Computing

In the domain of machine learning, least square twin support vector machine (LSTSVM) stands out as one of the state-of-the-art models. However, LSTSVM suffers from sensitivity to noise and outliers, overlooking the SRM principle and instability in resampling. Moreover, its computational complexity and reliance on matrix inversions hinder the efficient processing of large datasets. As a remedy to the aforementioned challenges, we propose the robust granular ball LSTSVM (GBLSTSVM). GBLSTSVM is trained using granular balls instead of original data points. The core of a granular ball is found at its center, where it encapsulates all the pertinent information of the data points within the ball of specified radius. To improve scalability and efficiency, we further introduce the large-scale GBLSTSVM (LS-GBLSTSVM), which incorporates the SRM principle through regularization terms. Experiments are performed on UCI, KEEL, and NDC benchmark datasets; both the proposed GBLSTSVM and LS-GBLSTSVM models consistently outperform the baseline models.

cs.LG↗
arXiv2025

GRVFL-MV: Graph Random Vector Functional Link Based on Multi-View Learning

The classification performance of the random vector functional link (RVFL), a randomized neural network, has been widely acknowledged. However, due to its shallow learning nature, RVFL often fails to consider all the relevant information available in a dataset. Additionally, it overlooks the geometrical properties of the dataset. To address these limitations, a novel graph random vector functional link based on multi-view learning (GRVFL-MV) model is proposed. The proposed model is trained on multiple views, incorporating the concept of multiview learning (MVL), and it also incorporates the geometrical properties of all the views using the graph embedding (GE) framework. The fusion of RVFL networks, MVL, and GE framework enables our proposed model to achieve the following: i) efficient learning: by leveraging the topology of RVFL, our proposed model can efficiently capture nonlinear relationships within the multi-view data, facilitating efficient and accurate predictions; ii) comprehensive representation: fusing information from diverse perspectives enhance the proposed model's ability to capture complex patterns and relationships within the data, thereby improving the model's overall generalization performance; and iii) structural awareness: by employing the GE framework, our proposed model leverages the original data distribution of the dataset by naturally exploiting both intrinsic and penalty subspace learning criteria. The evaluation of the proposed GRVFL-MV model on various datasets, including 27 UCI and KEEL datasets, 50 datasets from Corel5k, and 45 datasets from AwA, demonstrates its superior performance compared to baseline models. These results highlight the enhanced generalization capabilities of the proposed GRVFL-MV model across a diverse range of datasets.

cs.LG↗
arXiv2024

ACD codes over skew-symmetric dualities

The applications of additive codes mainly lie in quantum error correction and quantum computing. Due to their applications in quantum codes, additive codes have grown in importance. In addition to this, additive codes allow the implementation of a variety of dualities. The article begins by developing the properties of Additive Complementary Dual (ACD) codes with respect to arbitrary dualities over finite abelian groups. Further, we introduce a subclass of non-symmetric dualities referred to as skew-symmetric dualities. Then, we precisely count symmetric and skew-symmetric dualities over finite fields. Two conditions have been obtained: one is a necessary and sufficient condition, and the other is a necessary condition. The necessary and sufficient condition is for an additive code to be an ACD code over arbitrary dualities. The necessary condition is on the generator matrix of an ACD code over skew-symmetric dualities. We provide bounds for the highest possible minimum distance of ACD codes over skew-symmetric dualities. Finally, we find some new quaternary ACD codes over non-symmetric dualities with better parameters than the symmetric ones.

cs.IT↗
arXiv2024

Additive one-rank hull codes over finite fields

This article explores additive codes with one-rank hull, offering key insights and constructions. The article introduces a novel approach to finding one-rank hull codes over finite fields by establishing a connection between self-orthogonal elements and solutions of quadratic forms. It also provides a precise count of self-orthogonal elements for any duality over the finite field $\mathbb{F}_q$, particularly odd primes. Additionally, construction methods for small rank hull codes are introduced. The highest possible minimum distance among additive one-rank hull codes is denoted by $d_1[n,k]_{p^e,M}$. The value of $d_1[n,k]_{p^e,M}$ for $k=1,2$ and $n\geq 2$ with respect to any duality $M$ over any finite field $\mathbb{F}_{p^e}$ is determined. Furthermore, the new quaternary one-rank hull codes are identified over non-symmetric dualities with better parameters than symmetric ones.

cs.IT↗
arXiv2023

Construction Methods for Galois LCD codes over Finite Fields

In this article, first we present a method for constructing many Hermitian LCD codes from a given Hermitian LCD code, and then provide several methods which utilize either a given [n, k, d] linear code or a given [n, k, d] Galois LCD code to construct new Galois LCD codes with different parameters. Using these construction methods, we construct several new [n, k, d] ternary LCD codes with better parameters for $26\leq n \leq 40$, and $21 \leq k \leq 30$. Also, optimal 2-Galois LCD codes over $\mathbb{F}_{2^3}$ for code length, $1 \leq n \leq 15$ have been obtained. Finally, we extend some previously known results to the $σ$-inner product from Euclidean inner product.

cs.IT↗
arXiv2023

On pairs of $r$-primitive and $k$-normal elements with prescribed traces over finite fields

Given $\mathbb{F}_{q^{n}}$, a field with $q^n$ elements, where $q $ is a prime power and $n$ is positive integer. For $r_1,r_2,m_1,m_2 \in \mathbb{N}$, $k_1,k_2 \in \mathbb{N}\cup \{0\}$, a rational function $F = \frac{F_1}{F_2}$ in $\mathbb{F}_{q}[x]$ with deg($F_i$) $\leq m_i$; $i=1,2,$ satisfying some conditions, and $a,b \in \mathbb{F}_{q}$, we construct a sufficient condition on $(q,n)$ which guarantees the existence of an $r_1$-primitive, $k_1$-normal element $ε\in \mathbb{F}_{q^n}$ such that $F(ε)$ is $r_2$-primitive, $k_2$-normal with $\operatorname{Tr}_{\mathbb{F}_{q^n}/\mathbb{F}_q}(ε) = a$ and $\operatorname{Tr}_{\mathbb{F}_{q^n}/\mathbb{F}_q}(ε^{-1}) = b$. For $m_1=10, \; m_2=11,\; r_1 = 3, \; r_2 = 2, \; k_1=2,\;k_2 = 1$, we establish bounds on $q$, for various $n$, to determine the existence of such elements in $\mathbb{F}_{q^{n}}$. Furthermore, we identify all such pairs $(q,n)$ excluding 10 possible values of $(q,n)$, in fields of characteristics 13.

math.NT↗
arXiv2023

Existence of primitive pairs with two prescribed traces over finite fields

Given $F= \mathbb{F}_{p^{t}}$, a field with $p^t$ elements, where $p $ is a prime power, $t\geq 7$, $n$ are positive integers and $f=f_1/f_2$ is a rational function, where $f_1, f_2$ are relatively prime, irreducible polynomials with $deg(f_1) + deg(f_2) = n $ in $F[x]$. We construct a sufficient condition on $(p,t)$ which guarantees primitive pairing $(ε, f(ε))$ exists in $F$ such that $Tr_{\mathbb{F}_{p^t}/\mathbb{F}_p}(ε) = a$ and $Tr_{\mathbb{F}_{p^t}/\mathbb{F}_p}(f(ε)) = b$ for any prescribed $a,b \in \mathbb{F}_{p}$. Further, we demonstrate for any positive integer $n$, such a pair definitely exists for large $t$. The scenario when $n = 2$ is handled separately and we verified that such a pair exists for all $(p,t)$ except from possible 71 values of $p$. A result for the case $n=3$ is given as well.

math.NT↗
arXiv2022

Effect of magnetic phase coexistence on spin-phonon coupling and magnetoelectric effect in polycrystalline Sm0.5Y0.5Fe0.58Mn0.42O3

The polycrystalline co-doped samples of Sm0.5Y0.5Fe0.58Mn0.42O3 were prepared by solid-state reaction route and its various physical properties with their correlations have been investigated. The dc magnetization measurements on the sample revealed a weak ferromagnetic (WFM) transition at TN=361 K that is followed by an incomplete spin reorientation (SR) transition at TSR1= 348 K. A first order magnetic transition (FOMT) around 292 K completes the spin reorientation transition and the material enters into a nearly collinear antiferromagnetic (AFM) state for T < 260 K. The compound exhibited magnetization reversal below the compensation temperature (Tcomp) = 92 K at low measured field of 100 Oe. At further low temperature below 71 K, the compound also exhibited Zero-field cooled memory effects confirming a reentrant spinglass state formation. Robust magnetodielectric (MD) magnetoelectric coupling has been established in the present material through field dependent dielectric and resistivity measurements. True ferroelectric transition with a considerable value of saturation polarization (= 0.06 micro C/cm2 at 15 K) have been found in the specimen below TFE= 108 K. We observed an intense spin-phonon coupling (SPC) across TSR and TN from the temperature dependent Raman spectroscopy and is responsible for the intrinsic magnetoelectric effect. This SPC also stabilizes the ferroelectric state below TFE in the material. The delicate interplay of the lattice (Phonons), charge and spins governs the observed features in the investigated physical properties of the material that makes the specimen a promising multifunctional material.

cond-mat.mtrl-sci↗
arXiv2022

Multisecret-sharing scheme with two-level security and its applications in Blockchain

A $(t,m)$-threshold secret sharing and multisecret-sharing scheme based on Shamir's SSS are introduced with two-level security using a one-way function. Besides we give its application in smart contract-enabled consortium blockchain network. The proposed scheme is thoroughly examined in terms of security and efficiency. Privacy, security, integrity, and scalability are also analyzed while applying it to the blockchain network.

cs.CR↗
arXiv2022

Galois LCD Codes Over Fq + uFq + vFq + uvFq

In \cite{anote}, Wu and Shi studied $ l $-Galois LCD codes over finite chain ring $\mathcal{R}=\mathbb{F}_q+u\mathbb{F}_q$, where $u^2=0$ and $ q=p^e$ for some prime $p$ and positive integer $e$. In this work, we extend the results to the finite non chain ring $ \mathcal{R} =\mathbb{F}_q+u\mathbb{F}_q+v\mathbb{F}_q+uv\mathbb{F}_q$, where $u^2=u,v^2=v $ and $ uv=vu $. We define a correspondence between $ l $-Galois dual of linear codes over $ \mathcal{R} $ and $ l $-Galois dual of its component codes over $ \mathbb{F}_q .$ Further, we construct Euclidean LCD and $ l $-Galois LCD codes from linear code over $ \mathcal{R} $. This consequently leads us to prove that any linear code over $ \mathcal{R} $ is equivalent to Euclidean ($ q>3 $) and $ l $-Galois LCD ($0<l<e$, and $p^{e-l}+1\mid p^e-1$) code over $ \mathcal{R} .$ Finally, we investigate MDS codes over $ \mathcal{R} .$

cs.IT↗
arXiv2021

Combinatorial Large-area MoS2/Anatase-TiO2 interface: A Pathway to Emergent Optical and Opto-electronic Functionalities

Interface of transition metal dichalcogenide (TMDC) and high-k dielectric transition metal oxides (TMO) had triggerred umpteen discourses due to the indubitable impact of TMO in reducing the contact resistances and restraining the Fermi-level pinning for the metal-TMDC contacts. In the present work, we focus on the unresolved tumults of large-area TMDC/TMO interfaces, grown by adopting different techniques. Here, on a pulsed laser deposited (PLD) MoS2 thin film, a layer of TiO2 is grown by using both atomic layer deposition (ALD) and PLD. These two different techniques emanate TiO2 layers with different crystalline properties, thicknesses and interfacial morphologies, subsequently influencing the electronic and optical properties of the interfaces. In addition, they manifest a boost in the extent of p-type doping with increasing thickness of TiO2, as emerged after analyzing the core-level shifts of the X-ray photoelectron spectra (XPS). Density functional analysis of the MoS2/Anatase-TiO2 interfaces, for pristine and in presence of a wide range of interfacial defects, could explain the interdependence of doping and the terminating atomic-surface of TiO2 on MoS2. The optical properties of the interface, encompassing the photoluminescence, transient absorption and z-scan two-photon absorption indicate the presence of defect-induced localized mid-gap levels in MoS2/TiO2 (PLD), resulting quenched exciton signals. On the contrary, the relatively defect-free interface in MoS2/TiO2 (ALD) demonstrates a clear presence of both A and B excitons of MoS2. From the investigation of optical properties, we indicate that MoS2/TiO2 (PLD) interface may act as a promising saturable absorber. Moreover, MoS2/TiO2 (PLD) interface had resulted a better photo-transport. A potential application of MoS2/TiO2 (PLD) is demonstrated by the fabrication of a p-type photo-transistor with the ionic-gel top gate.

cond-mat.mtrl-sci↗
arXiv2021

Existence of Primitive Normal Pairs with One Prescribed Trace over Finite Fields

Given $m, n, q\in \mathbb{N}$ such that $q$ is a prime power and $m\geq 3$, $a\in \mathbb{F}_q$, we establish a sufficient condition for the existence of primitive pair $(α, f(α))$ in $\mathbb{F}_{q^m}$ such that $α$ is normal over $\mathbb{F}_q$ and $\text{Tr}_{\mathbb{F}_{q^m}/\mathbb{F}_q}(α^{-1})=a$, where $f(x)\in \mathbb{F}_{q^m}(x)$ is a rational function of degree sum $n$. Further, when $n=2$ and $q=5^k$ for some $k\in \mathbb{N}$, such a pair definitely exists for all $(q, m)$ apart from at most $20$ choices.

math.NT↗
arXiv2020

Run-time reconfigurable multi-precision floating point multiplier design for high speed, low-power applications

Floating point multiplication is one of the crucial operations in many application domains such as image processing, signal processing etc. But every application requires different working features. Some need high precision, some need low power consumption, low latency etc. But IEEE-754 format is not really flexible for these specifications and also design is complex. Optimal run-time reconfigurable hardware implementations may need the use of custom floating-point formats that do not necessarily follow IEEE specified sizes. In this paper, we present a run-time-reconfigurable floating point multiplier implemented on FPGA with custom floating point format for different applications. This floating point multiplier can have 6 modes of operations depending on the accuracy or application requirement. With the use of optimal design with custom IPs (Intellectual Properties), a better implementation is done by truncating the inputs before multiplication. And a combination of Karatsuba algorithm and Urdhva-Tiryagbhyam algorithm (Vedic Mathematics) is used to implement unsigned binary multiplier. This further increases the efficiency of the multiplier.

cs.AR↗
arXiv2020

Existence of Primitive Pairs with Prescribed Traces over Finite Fields

Let $F=\mathbb{F}_{q^m}$, $m>6$, $n$ a positive integer, and $f=p/q$ with $p$, $q$ co-prime irreducible polynomials in $F[x]$ and deg$(p)$ $+$ deg$(q)= n$. A sufficient condition has been obtained for the existence of primitive pairs $(α, f(α))$ in $F$ such that for any prescribed $a, b$ in $E=\mathbb{F}_q$, Tr$F/E (α) = a$ and Tr$F/E (α^{-1}) = b$. Further, for every positive integer $n$, such a pair definitely exists for large enough $(q,m)$. The case $n = 2$ is dealt separately and proved that such a pair exists for all $(q,m)$ apart from at most $64$ choices.

math.NT↗
arXiv2019

An efficient floating point multiplier design for high speed applications using Karatsuba algorithm and Urdhva-Tiryagbhyam algorithm

Floating point multiplication is a crucial operation in high power computing applications such as image processing, signal processing etc. And also multiplication is the most time and power consuming operation. This paper proposes an efficient method for IEEE 754 floating point multiplication which gives a better implementation in terms of delay and power. A combination of Karatsuba algorithm and Urdhva-Tiryagbhyam algorithm (Vedic Mathematics) is used to implement unsigned binary multiplier for mantissa multiplication. The multiplier is implemented using Verilog HDL, targeted on Spartan-3E and Virtex-4 FPGA.

cs.AR↗