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Om Prakash

Publications and source records attributed to Om Prakash.

At least 19 recordsLinked to original sources
arXiv2026

Revisiting In-Medium QCD Effects on Spin-Polarized Strange Quark Stars

We investigate the properties of exotic Strange Quark Matter with spin polarization and the complex configuration of Strange Quark Stars using a phenomenological MIT Bag Model, enhanced by incorporating a QCD informed running strange quark mass dependent on the chemical potential. The effective mass using quasiparticle approach is utilized to understand the framework of SQM. The resulting Equation of State is constructed for two distinct parameter sets, yielding an energy per baryon below the iron limit for stable configurations and thus supporting the Bodmer Witten Terazawa hypothesis that SQM could be the actual ground state of exotic matter. This framework is then used to address the Tolman Oppenheimer Volkoff equations to study the effect of spin polarization on stellar properties. The model predicts that the maximum stellar mass increases with the degree of spin polarization, a result that diverges from previous constant mass models. Furthermore, the model predictions for mass, radius, and surface redshift are in excellent agreement with observational constraints for the compact object Vela X one. This agreement validates our theoretical approach and strengthens the candidacy of Vela X one as a Strange Quark Star. Overall, the model results highlight the importance of in medium QCD effects in describing dense matter.

hep-ph↗
arXiv2026

Thermodynamical analysis of QGP using effective PNJL model with Quasiparticle approach

We study the thermodynamics of the quark-gluon plasma using an effective Two flavor Polyakov Nambu Jona Lasinio (PNJL) model extended by a quasiparticle description for quarks and gluons, incorporating temperature dependent quark masses within the PNJL framework. Two variants, Quasiparticle Model-I and Quasiparticle Model-II, are implemented to investigate bulk thermodynamic observables such as pressure, energy density, entropy density, specific heat, and the speed of sound. The combined framework yields a robust baseline for the description of hot QGP dynamics in the high temperature regime at vanishing chemical potential and zero magnetic field. Systematic comparison with lattice QCD results shows an excellent agreement and clear improvement over conventional PNJL implementations. We observe that both variants complement each other, offering mutually consistent insight into quasiparticle mass effects and medium response in the deconfined phase. This mutual consistency validates the physical foundation of the overall quasiparticle mechanism, reinforcing the credibility of the calculated Equation of State. Finally, the quasiparticle model extension improves PNJL from a descriptive tool to a more qualitative phenomenological approach, enabling an improved description of the strong interacting quark-gluon plasma.

hep-ph↗
arXiv2026

Construction of Cyclic Codes over a Class of Matrix Rings

Let $ \mathbb F_2[u]/ \langle u^k \rangle= \mathbb F_2+u\mathbb F_2+u^2\mathbb F_2+\cdots+u^{k-1}\mathbb F_2 ,$ where $u^k=0$ for a positive integer $k$, and $\mathcal{R}=M_4 (\mathbb F_2( u)/ \langle u^k \rangle)$ be the finite noncommutative non-chain matrix ring of order $4\times4$. This paper presents the construction of cyclic codes over the finite field $\mathbb F_{16}$ via the considered matrix ring $\mathcal{R}$. In this connection, first, we discuss the structure of the ring $\mathcal{R}$ and show that $\mathcal{R}$ is isomorphic to the ring $( \mathbb F_{16}+ v\mathbb F_{16} + v^2\mathbb F_{16} + v^3\mathbb F_{16}) + u(\mathbb F_{16} + v\mathbb F_{16} + v^2\mathbb F_{16} + v^3\mathbb F_{16}) + u^2(\mathbb F_{16} + v\mathbb F_{16} + v^2\mathbb F_{16}+ v^3\mathbb F_{16}) + \cdots + u^{k-1}(\mathbb F_{16} + v\mathbb F_{16} + v^2\mathbb F_{16} + v^3\mathbb F_{16})$ where $v^4=0, u^k=0, u^iv^j=v^ju^i$ for $i \in \{1,\dots, k-1\}$ and $j \in \{1, 2, 3\}$. Then, we establish the form of ideals of the ring $\mathcal{R}$ and related cyclic codes over $\mathcal{R}$. Further, we show that these cyclic codes can be written as the direct sums of $\mathcal{R}$-submodules of $\frac{\mathcal{R}[x]}{ }$, and derive the formula for the cardinality of cyclic codes over $\mathcal{R}$. Then, we consider the Euclidean and Hermitian duals of the derived cyclic codes over $\mathcal{R}$. Under the module isometry for $\mathcal{R}$, we use the Bachoc map and the Gray map, which takes a derived cyclic code over $\mathcal{R}$ to $\mathbb F_{16}$. Finally, we provide some non-trivial examples of linear codes over $\mathbb F_{16}$ with good parameters that support our derived results and compare a few codes with existing codes in the literature.

cs.IT↗
arXiv2026

Symplectic Hulls over a Non-Unital Ring

This paper presents the study of the symplectic hulls over a non-unital ring $ E= \langle \kappa,\tau \mid 2 \kappa =2 \tau=0,~ \kappa^2=\kappa,~ \tau^2=\tau,~ \kappa \tau=\kappa,~ \tau \kappa=\tau \rangle$. We first identify the residue and torsion codes of the left, right, and two-sided symplectic hulls, and characterize the generator matrix of the two-sided symplectic hull of a free $E$-linear code. Then, we explore the symplectic hull of the sum of two free $E$-linear codes. Subsequently, we provide two build-up techniques that extend a free $E$-linear code of smaller length and symplectic hull-rank to one of larger length and symplectic hull-rank. Further, for free $E$-linear codes, we discuss the permutation equivalence and investigate the symplectic hull-variation problem. An application of this study is given by classifying the free $E$-linear optimal codes for smaller lengths.

cs.IT↗
arXiv2025

On Maps that Preserve the Lie Products Equal to Fixed Elements

This work characterizes the general form of a bijective linear map $\Psi:\mathscr{M}_n(\mathbb{C}) \to \mathscr{M}_n(\mathbb{C})$ such that $[\Psi(A_1),~\Psi(A_2)]=D_2$ whenever $[A_1,~A_2]=D_1$ where $D_1~\text{and}~D_2$ are fixed matrices. Additionally, let $\mathscr{H}_1$ and $\mathscr{H}_2$ be the infinite-dimensional complex Hilbert spaces. We characterize the bijective linear map $\Psi: \mathscr{B}(\mathscr{H}_1) \to \mathscr{B}(\mathscr{H}_2)$ where $\Psi(A_1) \circ ~\Psi(A_2)=D_2$ whenever $A_1\circ ~A_2=D_1$ and $D_1~\text{and}~D_2$ are fixed operators.

math.RA↗
arXiv2025

Hulls of Free Linear Codes over a Non-Unital Ring

This paper investigates the hull codes of free linear codes over a non-unital ring $ E= \langle \kappa,\tau \mid 2 \kappa =2 \tau=0,~ \kappa^2=\kappa,~ \tau^2=\tau,~ \kappa \tau=\kappa,~ \tau \kappa=\tau \rangle$. Initially, we examine the residue and torsion codes of various hulls of $E$-linear codes and obtain an explicit form of the generator matrix of the hull of a free $E$-linear code. Then, we propose four build-up construction methods to construct codes with a larger length and hull-rank from codes with a smaller length and hull-rank. Some illustrative examples are also given to support our build-up construction methods. Subsequently, we study the permutation equivalence of two free $E$-linear codes and discuss the hull-variation problem. As an application, we classify optimal free $E$-linear codes for lengths up to $8$.

cs.IT↗
arXiv2025

Enhancing the Plasmonic Hotspot Density via Structural Engineering of Multi-layered MoO3-Ag-Au Systems Under Extreme Electronic Excitation Conditions for Ultra-Sensitive SERS Applications

We illustrate ion-beam engineering of MoO3 Ag Au multilayer plasmonic substrates to improve SERS performance, We illustrate ion-beam engineering of MoO3-Ag-Au multilayer plasmonic substrates to improve SERS performance. Orthorhombic α-MoO3 microflakes were produced via chemical vapour deposition (CVD) on Si-SiO2 substrates. Thin films of Ag (5 nm) and Au (5 nm) were thermally evaporated onto the MoO3 flakes, and the samples were subjected to 100 MeV Ag8+ swift heavy ion irradiation at fluences of 3e11 and 3e12 ions cm-2. Irradiation causes dewetting of metal films, prompting structural and morphological changes that result in the formation of dispersed Ag-Au nanoparticles, enhanced surface roughness, and defect generation within the MoO3 lattice. X-ray diffraction (XRD) verifies the α-MoO3 phase; field emission scanning electron microscopy (FESEM) elucidates nanoparticle formation and surface reorganisation; Raman spectroscopy and X-ray photoelectron spectroscopy (XPS) disclose vibrational alterations and binding-energy shifts in Mo 3d, indicative of oxygen vacancies (V_O) and partial reduction of Mo. SERS measurements of molecular probes demonstrate significantly increased Raman intensities following ion irradiation.

cond-mat.mtrl-sci↗
arXiv2025

On The Roots of Independence Polynomial: Quantifying The Gap

The independence polynomial of a graph $G$ is the generating polynomial corresponding to its independent sets of different sizes. More formally, if $a_k(G)$ denotes the number of independent sets of $G$ of size $k$ then \[I(G,z) \as \sum_{k}^{} (-1)^k a_k(G) z^k.\] The study of evaluating $I(G,z)$ has several deep connections to problems in combinatorics, complexity theory and statistical physics. Consequently, the roots of the independence polynomial have been studied in detail. In particular, many works have provided regions in the complex plane that are devoid of any roots of the polynomial. One of the first such results showed a lower bound on the absolute value of the smallest root $β(G)$ of the polynomial. Furthermore, when $G$ is connected, Goldwurm and Santini established that $β(G)$ is a simple real root of $I(G,z)$ smaller than one. An alternative proof was given by Csikvári. Both proofs do not provide a gap from $β(G)$ to the smallest absolute value amongst all the other roots of $I(G,z)$. In this paper, we quantify this gap.

math.CO↗
arXiv2025

Additivity of multiplicative (generalized) maps over rings

In this paper, we mainly prove some results on the additivity of maps over rings under certain conditions. First, we discuss a special case of MARTINDALE III's theorem of \cite{1969M} as a bijective map $φ$ over a ring $R$ with a non-trivial idempotent satisfying $φ(ab)=φ(a)φ(b)$ for all $a, b\in R$, is additive. Then we prove that a map $D$ on $R$ satisfying $D(ab)=D(a)b+φ(a) D(b)$ for all $a,b\in R$, where $φ$ is the map mentioned above, is additive. Finally, we establish that if a map $g$ over $R$ satisfies $g(ab)=g(a)b+φ(a)D(b),$ for all $a,b\in R$ and the maps $φ$ and $D$ are mentioned above, then $g$ is additive.

math.RA↗
arXiv2025

Skew generalized quasi-cyclic codes over non-chain ring $F_q+vF_q$

For a prime $p$, let $F_q$ be the finite field of order $q= p^d$. This paper presents the study on skew generalized quasi-cyclic (SGQC) codes of length $n$ over the non-chain ring $F_q+vF_q$ where $v^2=v$ and $θ_t$ is the Galois automorphism. Here, first, we prove the dual of an SGQC code of length $n$ is also an SGQC code of the same length and derive a necessary and sufficient condition for the existence of a self-dual SGQC code. Then, we discuss the $1$-generator polynomial and the $ρ$-generator polynomial for skew generalized quasi-cyclic codes. Further, we determine the dimension and BCH type bound for the 1-generator skew generalized quasi-cyclic codes. As a by-product, with the help of MAGMA software, we provide a few examples of SGQC codes and obtain some $2$-generator SGQC codes of index $2$.

cs.IT↗
arXiv2025

Native-oxide-passivated trilayer junctions for superconducting qubits

Superconducting qubits in today's quantum processing units are typically fabricated with angle-evaporated aluminum--aluminum-oxide--aluminum Josephson junctions. However, there is an urgent need to overcome the limited reproducibility of this approach when scaling up the number of qubits and junctions. Fabrication methods based on subtractive patterning of superconductor--insulator--superconductor trilayers, used for more classical large-scale Josephson junction circuits, could provide the solution but they in turn often suffer from lossy dielectrics incompatible with high qubit coherence. In this work, we utilize native aluminum oxide as a sidewall passivation layer for junctions based on aluminum--aluminum-oxide--niobium trilayers, and use such junctions in qubits. We design the fabrication process such that the few-nanometer-thin native oxide is not exposed to oxide removal steps that could increase its defect density or hinder its ability to prevent shorting between the leads of the junction. With these junctions, we design and fabricate transmon-like qubits and measure time-averaged coherence times up to 30 $\mu$s at a qubit frequency of 5 GHz, corresponding to a qubit quality factor of one million. Our process uses subtractive patterning and optical lithography on wafer scale, enabling high throughput in patterning. This approach provides a scalable path toward fabrication of superconducting qubits on industry-standard platforms.

quant-ph↗
arXiv2025

Encoding and Construction of Quantum Codes from $(γ,Δ)$-cyclic Codes over a Class of Non-chain Rings

Let $\mathbb{F}_q$ be a finite field of $q=p^m$ elements where $p$ is a prime and $m$ is a positive integer. This paper considers $(γ,Δ)$-cyclic codes over a class of finite non-chain commutative rings $\mathscr{R}_{q,s}=\mathbb{F}_q[v_1,v_2,\dots,v_s]/\langle v_i-v_i^2,v_iv_j=v_jv_i=0\rangle$ where $γ$ is an automorphism of $\mathscr{R}_{q,s}$, $Δ$ is a $γ$-derivation of $\mathscr{R}_{q,s}$ and $1\leq i\neq j\leq s$ for a positive integer $s$. Here, we show that a $(γ,Δ)$-cyclic code of length $n$ over $\mathscr{R}_{q,s}$ is the direct sum of $(θ,\Im)$-cyclic codes of length $n$ over $\mathbb{F}_q$, where $θ$ is an automorphism of $\mathbb{F}_q$ and $\Im$ is a $θ$-derivation of $\mathbb{F}_q$. Further, necessary and sufficient conditions for both $(γ,Δ)$-cyclic and $(θ,\Im)$-cyclic codes to contain their Euclidean duals are established. Then, we obtain many quantum codes by applying the dual containing criterion on the Gray images of these codes. These codes have better parameters than those available in the literature. Finally, the encoding and error-correction procedures for our proposed quantum codes are discussed.

cs.IT↗
arXiv2025

DNA codes from $(\text{\textbaro}, \mathfrak{d}, γ)$-constacyclic codes over $\mathbb{Z}_4+ω\mathbb{Z}_4$

This work introduces a novel approach to constructing DNA codes from linear codes over a non-chain extension of $\mathbb{Z}_4$. We study $(\text{\textbaro},\mathfrak{d}, γ)$-constacyclic codes over the ring $\mathfrak{R}=\mathbb{Z}_4+ω\mathbb{Z}_4, ω^2=ω,$ with an $\mathfrak{R}$-automorphism $\text{\textbaro}$ and a $\text{\textbaro}$-derivation $\mathfrak{d}$ over $\mathfrak{R}.$ Further, we determine the generators of the $(\text{\textbaro},\mathfrak{d}, γ)$-constacyclic codes over the ring $\mathfrak{R}$ of any arbitrary length and establish the reverse constraint for these codes. Besides the necessary and sufficient criterion to derive reverse-complement codes, we present a construction to obtain DNA codes from these reversible codes. Moreover, we use another construction on the $(\text{\textbaro},\mathfrak{d},γ)$-constacyclic codes to generate additional optimal and new classical codes. Finally, we provide several examples of $(\text{\textbaro},\mathfrak{d}, γ)$ constacyclic codes and construct DNA codes from established results. The parameters of these linear codes over $\mathbb{Z}_4$ are better and optimal according to the codes available at \cite{z4codes}.

cs.IT↗
arXiv2025

Skew Generalized Polycyclic Codes with Derivations

In this paper, we first consider the iterated skew polynomial ring $\mathscr{R}[z_1;τ_1,δ_{τ_1}]$\\$[z_2;τ_2,δ_{τ_2}]$, where $\mathscr{R}$ is a finite ring with unity. Then we use this structure for the construction of skew generalized polycyclic codes over the ring $\mathscr{R}$ and finite field $\mathbb{F}_q$, where $q=p^m$ for some positive integer $m$. Further, we derive the structure of the generator and parity check matrices for skew generalized polycyclic codes. Furthermore, we improve the Bose-Chaudhuri-Hocquenghem (BCH) lower bound for a minimum distance of skew generalized polycyclic codes with non-zero derivations over a finite field. Moreover, we find a sufficient condition for a code to be a maximum-distance-separable (MDS) code. In addition, we provide examples of MDS codes to show the importance of our results. A comparative summary of our work with other linear codes is also discussed.

cs.IT↗
arXiv2025

Classification of LCD and self-dual codes over a finite non-unital local ring

This work explores LCD and self-dual codes over a noncommutative non-unital ring $ E_p= \langle r,s ~|~ pr =ps=0,~ r^2=r,~ s^2=s,~ rs=r,~ sr=s \rangle$ of order $p^2$ where $p$ is a prime. Initially, we study the monomial equivalence of two free $E_p$-linear codes. In addition, a necessary and sufficient condition is derived for a free $E_p$-linear code to be MDS and almost MDS (shortly AMDS). Then, we use these results to classify MDS and AMDS LCD codes over $E_2$ and $E_3$ under monomial equivalence for lengths up to $6$. Subsequently, we study left self-dual codes over the ring $E_p$ and classify MDS and AMDS left self-dual codes over $E_2$ and $E_3$ for lengths up to $12$. Finally, we study self-dual codes over the ring $E_p$ and classify MDS and AMDS self-dual codes over $E_2$ and $E_3$ for short lengths.

cs.IT↗
arXiv2024

Commuting Jordan derivations over a Ring with idempotents

This paper explores the behaviour of commuting Jordan derivations over prime rings with non-trivial idempotents and demonstrates that they become zero maps. Further, it establishes this result for commuting Jordan higher derivations over prime rings under specific conditions. In fact, it introduces commuting generalized Jordan derivations over rings and establishes that the zero map is the only commuting generalized Jordan derivation over prime rings under certain assumptions.

math.RA↗
arXiv2024

Galois hulls of constacyclic codes over affine algebra rings

Let $\mathcal A$ the affine algebra given by the ring $\mathbb{F}_q[X_1,X_2,\ldots,X_\ell]/ I$, where $I$ is the ideal $\langle t_1(X_1), t_2(X_2), \ldots, t_\ell(X_\ell) \rangle$ with each $t_i(X_i)$, $1\leq i\leq \ell$, being a square-free polynomial over $\mathbb{F}_q$. This paper studies the $k$-Galois hulls of $λ$-constacyclic codes over $\mathcal A$ regarding their idempotent generators. For this, first, we define the $k$-Galois inner product over $\mathcal A$ and find the form of the generators of the $k$-Galois dual and the $k$-Galois hull of a $λ$-constacyclic code over $\mathcal A$. Then, we derive a formula for the $k$-Galois hull dimension of a $λ$-constacyclic code. Further, we provide a condition for a $λ$-constacyclic code to be $k$-Galois LCD. Finally, we give some examples of the use of these codes in constructing entanglement-assisted quantum error-correcting codes.

cs.IT↗