O. Prakash

activity

20172024

most citedOn ZpZp[u, v]-additive cyclic and constacyclic codes

1 citations · 2 across the 25 of their papers we have counts for

collaborators

26 papers

cs.IT2024

Galois hulls of constacyclic codes over affine algebra rings

Indibar Debnath, Habibul Islam, Edgar Martínez-Moro +1

Let $A$ the affine algebra given by the ring $F_{q} [X_{1}, X_{2}, \dots, X_{ℓ}] / I$ , where $I$ is the ideal $⟨ t_{1} (X_{1}), t_{2} (X_{2}), \dots, t_{ℓ} (X_{ℓ})⟩$ …

cs.IT2023

$F_{q} R$ -skew cyclic codes and their application to quantum codes

Om Prakash, Shikha Patel, Habibul Islam

Let $p$ be a prime and $F_{q}$ be the finite field of order $q = p^{m}$ . In this paper, we study $F_{q} R$ -skew cyclic codes where $\mathcal{R}=\mathbb{F}_q+u\ma…

math.RA2023

Additivity of multiplicative (generalized) skew semi-derivations on rings

Sk. Aziz, Arindam Ghosh, Om Prakash

In this paper, we introduce a new class of derivations that generalizes skew derivations and semi-derivations, and we call it ``skew semi-derivation". Further, we present a study o…

math.RA2023

Additivity of multiplicative (generalized) maps over rings

Sk Aziz, Arindam Ghosh, Om Prakash

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{196…

math.NT2023

Generalized Fruit Diophantine equation and Hyperelliptic curves

Om Prakash, Kalyan Chakraborty

We show the insolvability of the Diophantine equation $a x^{d} - y^{2} - z^{2} + x y z - b = 0$ in $Z$ for fixed $a$ and $b$ such that $a \equiv 1 (mod 12)$ and $b = 2^{d} a - 3$ , where $d$ is an…

math.RA2023

Some generalized Jordan maps on triangular rings force additivity

Sk Aziz, Arindam Ghosh, Om Prakash

In this paper, we show that a map $δ$ over a triangular ring $T$ satisfying $δ (ab + ba) = δ (a) b + a τ (b) + δ (b) a + b τ (a)$ , for all $a, b \in T$ and for some maps $τ$ over $…

cs.IT2022

Quantum Codes from additive constacyclic codes over a mixed alphabet and the MacWilliams identities

Indibar Debnath, Ashutosh Singh, Om Prakash +1

Let $Z_{p}$ be the ring of integers modulo a prime number $p$ where $p - 1$ is a quadratic residue modulo $p$ . This paper presents the study of constacyclic codes over chain r…

math.NT2022

A note on class number of certain real cyclotomic field

Om Prakash

We construct an infinite family of real cyclotomic fields with non-trivial class group. This result generalizes the result in [1] in the sense that our family includes theirs.

cs.IT2021★ 1 cited

Cyclic codes over a non-chain ring $R_{e, q}$ and their application to LCD codes

Habibul Islam, Edgar Martínez-Moro, Om Prakash

Let $F_{q}$ be a finite field of order $q$ , a prime power integer such that $q = e t + 1$ where $t \geq 1, e \geq 2$ are integers. In this paper, we study cyclic codes of length $n$ …

cs.IT2020

New non-binary quantum codes from skew constacyclic codes over the ring $F_{p^{m}} + v F_{p^{m}} + v^{2} F_{p^{m}}$

Ram Krishna Verma, Om Prakash, Ashutosh Singh

In this article, we construct new non-binary quantum codes from skew constacyclic codes over finite commutative non-chain ring $\mathcal{R}= \mathbb{F}_{p^m}[v]/\langle v^3 =v \ran…

math.RA2020

New Results on Generalization of Jordan centralizers over matrix rings

Arindam Ghosh, Om Prakash, Sushma Singh

This paper presents a study on Jordan maps over matrix rings with some functional equations related to additive maps on these rings. We first show that every Jordan left (right) ce…

cs.IT2019

Constacyclic codes of length $4 p^{s}$ over the Galois ring $GR (p^{a}, m)$

Om Prakash, Habibul Islam, Ram Krishna Verma

For prime $p$ , $GR (p^{a}, m)$ represents the Galois ring of order $p^{am}$ and characterise $p$ , where $a$ is any positive integer. In this article, we study the Type (1) $λ$ -constacy…

cs.IT2019

Reversible cyclic codes over $F_{q} + u F_{q}$

Om Prakash, Shikha Patel, Shikha Yadav

Let $q$ be a power of a prime $p$ . In this paper, we study reversible cyclic codes of arbitrary length over the ring $R = F_{q} + u F_{q}$ , where $u^{2} = 0 m o d q$ . Firs…

cs.IT2019

Skew Generalized Polycyclic Codes with Derivations

Shikha Patel, Om Prakash

In this paper, we first consider the iterated skew polynomial ring $R [z_{1}; τ_{1}, δ_{τ_{1}}]$ \$[z_2;τ_2,δ_{τ_2}] $, w h er e$ \mathscr{R}$ is a finite ring with unity. Then we use…

cs.IT2019★ 1 cited

On ZpZp[u, v]-additive cyclic and constacyclic codes

Habibul Islam, Om Prakash

Let $Z_{p}$ be the ring of residue classes modulo a prime $p$ . The $Z_{p} Z_{p} [u, v]$ -additive cyclic codes of length $(α, β)$ is identify as $\mathbb{Z}_{…

cs.LO2019

Parameterised Counting in Logspace

Anselm Haak, Arne Meier, Om Prakash +1

In this paper, we introduce a new framework for parameterised counting in logspace, inspired by the parameterised space bounded models developed by Elberfeld, Stockhusen and Tantau…

math.CO2018

Adjacency Matrix and Energy of the Line Graph of $Γ (Z_{n})$

Sheela Suthar, Om Prakash

Let $Γ (Z_{n})$ be the zero divisor graph of the commutative ring $Z_{n}$ and $L (Γ (Z_{n}))$ be the line graph of $Γ (Z_{n})$ . In this paper, we discuss ab…

math.CO2018

Pancyclic zero divisor graph over the ring $Z_{n} [i]$

Ravindra Kumar, Om Prakash

Let $Γ (Z_{n} [i])$ be the zero divisor graph over the ring $Z_{n} [i]$ . In this article, we study pancyclic properties of $Γ (Z_{n} [i])$ and $\overline{Γ(\mathbb{…

math.RA2018

Generalized (m,n)-Jordan centralizers and derivations on semiprime rings

Arindam Ghosh, Om Prakash

In this article, we prove Conjecture $1$ posed in 2013 by Fo $s ˇ$ ner \cite{fos} and Conjecture $1$ posed in 2014 by Ali and Fo $s ˇ$ ner \cite{ali} related to generalized…

math.RA2018

Jordan left {g, h}-derivations over some algebras

Arindam Ghosh, Om Prakash

In this article, left {g, h}-derivation and Jordan left {g, h}-derivation on algebras are introduced. It is shown that there is no Jordan left {g, h}-derivation over $\mathcal{M}_n…

math.RA2018

Jordan {g, h}-derivations on algebra of matrices

Arindam Ghosh, Om Prakash

In this article, we show that every Jordan {g, h}-derivation over T_n(C) is a {g, h}-derivation under an assumption, where C is a commutative ring with unity 1 not equal to 0. We g…

math.RA2018

Remarks on Jordan derivations over matrix algebras

Arindam Ghosh, Om Prakash

Let C be a commutative ring with unity. In this article, we show that every Jordan derivation over an upper triangular matrix algebra T_n(C) is an inner derivation. Further, we ext…

cs.IT2018

Skew cyclic codes over F_{p}+uF_{p}+\dots +u^{k-1}F_{p}

Om Prakash, Habibul Islam

In this article, we study the skew cyclic codes over R_{k}=F_{p}+uF_{p}+\dots +u^{k-1}F_{p} of length n. We characterize the skew cyclic codes of length $n$ over R_{k} as free left…

math.CO2017

Divisor graph of complement of Gamma(R)

Ravindra Kumar, Om Prakash

Let overline{Γ(R)} be the complement of zero divisor graph of a finite commutative ring R. In this article, we have provided the answer of the question (ii) raised by Osba and Alka…

Galois hulls of constacyclic codes over affine algebra rings

Fq​R-skew cyclic codes and their application to quantum codes

Additivity of multiplicative (generalized) skew semi-derivations on rings

Additivity of multiplicative (generalized) maps over rings

Generalized Fruit Diophantine equation and Hyperelliptic curves

Some generalized Jordan maps on triangular rings force additivity

Quantum Codes from additive constacyclic codes over a mixed alphabet and the MacWilliams identities

A note on class number of certain real cyclotomic field

Cyclic codes over a non-chain ring Re,q​ and their application to LCD codes

New non-binary quantum codes from skew constacyclic codes over the ring Fpm​+vFpm​+v2Fpm​

New Results on Generalization of Jordan centralizers over matrix rings

Constacyclic codes of length 4ps over the Galois ring GR(pa,m)

Reversible cyclic codes over Fq​+uFq​

Skew Generalized Polycyclic Codes with Derivations

On ZpZp[u, v]-additive cyclic and constacyclic codes

Parameterised Counting in Logspace

Adjacency Matrix and Energy of the Line Graph of Γ(Zn​)

Pancyclic zero divisor graph over the ring Zn​[i]

Generalized (m,n)-Jordan centralizers and derivations on semiprime rings

Jordan left {g, h}-derivations over some algebras

Jordan {g, h}-derivations on algebra of matrices

Remarks on Jordan derivations over matrix algebras

Skew cyclic codes over F_{p}+uF_{p}+\dots +u^{k-1}F_{p}

Divisor graph of complement of Gamma(R)

$F_{q} R$ -skew cyclic codes and their application to quantum codes

Cyclic codes over a non-chain ring $R_{e, q}$ and their application to LCD codes

New non-binary quantum codes from skew constacyclic codes over the ring $F_{p^{m}} + v F_{p^{m}} + v^{2} F_{p^{m}}$

Constacyclic codes of length $4 p^{s}$ over the Galois ring $GR (p^{a}, m)$

Reversible cyclic codes over $F_{q} + u F_{q}$

Adjacency Matrix and Energy of the Line Graph of $Γ (Z_{n})$

Pancyclic zero divisor graph over the ring $Z_{n} [i]$