M. Raka

activity

20142024

most citedPolyadic cyclic codes over a non-chain ring

F_{q} [u, v] / ⟨ f (u), g (v), uv - v u ⟩

3 citations · 7 across the 12 of their papers we have counts for

collaborators

14 papers

math.NT2024

Positive values of non-homogeneous quadratic forms of type (1,4): A conjecture of Bambah, Dumir and Hans-Gill

Swati Bhardwaj, Leetika Kathuria, Madhu Raka

Let $Q (x_{1}, \dots, x_{n})$ be a real indefinite quadratic form of the type $(r, s)$ , $n = r + s$ , signature $σ = r - s$ and determinant $D \neq = 0$ . Let $Γ_{r, n - r}$ denote the infimum of all nu…

cs.IT2022★ 1 cited

New Quantum codes from constacyclic codes over a general non-chain ring

Swati Bhardwaj, Mokshi Goyal, Madhu Raka

Let $q$ be a prime power and let $R = F_{q} [u_{1}, u_{2}, \dots, u_{k}] / ⟨ f_{i} (u_{i}), u_{i} u_{j} - u_{j} u_{i} ⟩$ be a finite non-chain ring, where $f_i(u_i), 1\leq i \leq…

cs.IT2022

Skew Cyclic Codes Over A Finite Ring : A Note on a result of Mohammadi et al

Swati Bhardwaj, Madhu Raka

In this small note we correct an error made by Mohammadi et al. in their paper entitled "On Skew Cyclic Codes Over A Finite Ring" ( Iranian Jl. Math. Sci. Inform. Vol 14 (1) (2019)…

cs.IT2022

Multi-dimensional Constacyclic Codes of Arbitrary Length over Finite Fields

Swati Bhardwaj, Madhu Raka

Multi-dimensional cyclic code is a natural generalization of cyclic code. In an earlier paper we explored two-dimensional constacyclic codes over finite fields. Following the same…

math.NT2020

On conjectures of Minkowski and Woods for $n = 10$

Leetika Kathuria, Madhu Raka

Let $L$ be a lattice in $n$ -dimensional Euclidean space $R^{n}$ reduced in the sense of Korkine and Zolotareff and having a basis of the form $(A_{1}, 0, 0, \dots$ $,0…

cs.IT2020

Two Dimensional $(α, β)$ -Constacyclic Codes of arbitrary length over a Finite Field

Swati Bhardwaj, Madhu Raka

In this paper we characterize the algebraic structure of two-dimensional $(α, β)$ -constacyclic codes of arbitrary length $s . ℓ$ and of their duals. For $α, β \in {1, - 1}$ , we give…

cs.IT2019

Skew constacyclic codes over a non-chain ring $F_{q} [u, v] / ⟨ f (u), g (v), uv - v u ⟩$

Swati Bhardwaj, Madhu Raka

Let $f (u)$ and $g (v)$ be two polynomials of degree $k$ and $ℓ$ respectively, not both linear, which split into distinct linear factors over $F_{q}$ . Let $\mathcal{R}=\m…

cs.IT2018★ 3 cited

Polyadic cyclic codes over a non-chain ring $F_{q} [u, v] / ⟨ f (u), g (v), uv - v u ⟩$

Mokshi Goyal, Madhu Raka

Let $f (u)$ and $g (v)$ be any two polynomials of degree $k$ and $ℓ$ respectively ( $k$ and $ℓ$ are not both $1$ ), which split into distinct linear factors over $F_{q}$ …

cs.IT2018

Duadic negacyclic codes over a finite non-chain ring and their Gray images

Mokshi Goyal, Madhu Raka

Let $f (u)$ be a polynomial of degree $m, m \geq 2,$ which splits into distinct linear factors over a finite field $F_{q}$ . Let $\mathcal{R}=\mathbb{F}_{q}[u]/\langle f(u)\…

math.NT2018

Good integers : A note on results of Jitman and Prugsapitak

Madhu Raka

In this paper, we fix some errors made by Jitman [1] and by Prugsapitak and Jitman [3] while characterizing good integers and $2^{β}$ -good integers.

math.NT2016★ 1 cited

Quadratic residue codes over the ring $F_{p} [u] / ⟨ u^{m} - u ⟩$ and their Gray images

Mokshi Goyal, Madhu Raka

Let $m \geq 2$ be any natural number and let $R = F_{p} + u F_{p} + u^{2} F_{p} + \dots + u^{m - 1} F_{p}$ be a finite non-chain ring, where $u^{m} = u$ an…

math.NT2015

$(1 - 2 u^{3})$ -constacyclic codes and quadratic residue codes over $F_{p} [u] / ⟨ u^{4} - u ⟩$

Madhu Raka, Leetika Kathuria, Mokshi Goyal

Let $R = F_{p} + u F_{p} + u^{2} F_{p} + u^{3} F_{p}$ with $u^{4} = u$ be a finite non-chain ring, where $p$ is a prime congruent to $1$ modulo $3$ . In t…

math.NT2015

Refined Estimates on Conjectures of Woods and Minkowski

Leetika Kathuria, Madhu Raka

Let $\land$ be a lattice in $R^{n}$ reduced in the sense of Korkine and Zolotareff having a basis of the form $(A_{1}, 0, 0, \dots, 0), (a_{2, 1}, A_{2}, 0, \dots, 0)$ , $\ldots,(a_{n,1…

math.NT2014★ 2 cited

On Conjectures of Minkowski and Woods for n=9

Leetika Kathuria, Madhu Raka

Let $R^{n}$ be the n-dimensional Euclidean space with $O$ as the origin. Let $\land$ be a lattice of determinant $1$ such that there is a sphere $∣ X ∣ < R$ which contains no p…

Positive values of non-homogeneous quadratic forms of type (1,4): A conjecture of Bambah, Dumir and Hans-Gill

New Quantum codes from constacyclic codes over a general non-chain ring

Skew Cyclic Codes Over A Finite Ring : A Note on a result of Mohammadi et al

Multi-dimensional Constacyclic Codes of Arbitrary Length over Finite Fields

On conjectures of Minkowski and Woods for n=10

Two Dimensional (α,β)-Constacyclic Codes of arbitrary length over a Finite Field

Skew constacyclic codes over a non-chain ring Fq​[u,v]/⟨f(u),g(v),uv−vu⟩

Polyadic cyclic codes over a non-chain ring Fq​[u,v]/⟨f(u),g(v),uv−vu⟩

Duadic negacyclic codes over a finite non-chain ring and their Gray images

Good integers : A note on results of Jitman and Prugsapitak

Quadratic residue codes over the ring Fp​[u]/⟨um−u⟩ and their Gray images

(1−2u3)-constacyclic codes and quadratic residue codes over Fp​[u]/⟨u4−u⟩

Refined Estimates on Conjectures of Woods and Minkowski

On Conjectures of Minkowski and Woods for n=9

On conjectures of Minkowski and Woods for $n = 10$

Two Dimensional $(α, β)$ -Constacyclic Codes of arbitrary length over a Finite Field

Skew constacyclic codes over a non-chain ring $F_{q} [u, v] / ⟨ f (u), g (v), uv - v u ⟩$

Polyadic cyclic codes over a non-chain ring $F_{q} [u, v] / ⟨ f (u), g (v), uv - v u ⟩$

Quadratic residue codes over the ring $F_{p} [u] / ⟨ u^{m} - u ⟩$ and their Gray images

$(1 - 2 u^{3})$ -constacyclic codes and quadratic residue codes over $F_{p} [u] / ⟨ u^{4} - u ⟩$