Dr. Manjit Singh

@dcrustm.ac.in

Professor (Assistant) Department of Mathematics
Deenbandhu Chhotu Ram University of Scinece and Technology, Murthal 131039, Sonepat, India

Dr. Manjit Singh


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https://researchid.co/manjit123
Graduation: University (Pt. Neki Ram recently) College Rohtak, Master Degree: M D University, Rohtak, PhD. DCRUST Murthal, Sonepat, Haryana

EDUCATION

PhD (Mathematics)

RESEARCH, TEACHING, or OTHER INTERESTS

Mathematics, Algebra and Number Theory, Discrete Mathematics and Combinatorics, Theoretical Computer Science

FUTURE PROJECTS

Factorization of polynomials over finite fields

The irreducible factors of order $ are useful in describing cyclic codes of length $. Several issues related to the above objective need to be addressed for the purpose, and I have been working on them for 10 years.


Applications Invited
9

Scopus Publications

Scopus Publications

  • Computing factors of cyclotomic polynomials over finite fields
    Deepak Sehrawat, Manjit Singh
    Journal of Algebraic Combinatorics, 2025
  • The set of representatives and explicit factorization of xn − 1 over finite fields
    Manjit Singh, Deepak
    Journal of Algebra and Its Applications, 2025
    Let [Formula: see text] be a positive integer and let [Formula: see text] be a finite field with [Formula: see text] elements, where [Formula: see text] is a prime power and [Formula: see text]. In this paper, we give the explicit factorization of [Formula: see text] over [Formula: see text] and count the number of its irreducible factors for the following conditions: [Formula: see text] are odd and [Formula: see text]. First, we present a method to obtain the set of all representatives of [Formula: see text]-cyclotomic cosets modulo [Formula: see text], where [Formula: see text]. This set of representatives is then used to find the irreducible factors of [Formula: see text] and the cyclotomic polynomial [Formula: see text] over [Formula: see text]. The form of irreducible factors of [Formula: see text] is characterized such that the coefficients of these irreducible factors are followed by second-order linear recurring sequences.
  • Equal-degree factorization of binomials and trinomials over finite fields
    Manjit Singh, Deepak Sehrawat
    Journal of Applied Mathematics and Computing, 2024
  • A Generalized Solution Approach to Matrix Games with 2-Tuple Linguistic Payoffs
    Rajkumar Verma, Manjit Singh, José M. Merigó
    Advances in Intelligent Systems and Computing, 2021
  • Linear Recurring Sequences and Explicit Factors of x2nd- 1 in Fq[ x ]
    Manjit Singh
    Algebra Colloquium, 2020
    Let 𝔽q be a finite field of odd characteristic containing q elements, and n be a positive integer. An important problem in finite field theory is to factorize xn − 1 into the product of irreducible factors over a finite field. Beyond the realm of theoretical needs, the availability of coefficients of irreducible factors over finite fields is also very important for applications. In this paper, we introduce second order linear recurring sequences in 𝔽q and reformulate the explicit factorization of [Formula: see text] over 𝔽q in such a way that the coefficients of its irreducible factors can be determined from these sequences when d is an odd divisor of q + 1.
  • A class of constacyclic codes containing formally self-dual and isodual codes
    Manjit SİNGH
    Journal of Algebra Combinatorics Discrete Structures and Applications, 2020
    In this paper, we investigate a class of constacyclic codes which contains isodual codes and formally self-dual codes. Further, we introduce a recursive approach to obtain the explicit factorization of $x^{2^m\\ell^n}-\\mu_k\\in\\mathbb{F}_q[x]$, where $n, m$ are positive integers and $\\mu_k$ is an element of order $\\ell^k$ in $\\mathbb{F}_q$. Moreover, we give many examples of interesting isodual and formally self-dual constacyclic codes.
  • Some subgroups of F*q and explicit factors of x2nd-1 ∈ q[x]
    Transactions on Combinatorics, 2019
  • Weight distribution of a class of cyclic codes of length 2 n
    Manjit SİNGH, Sudhir BATRA
    Journal of Algebra Combinatorics Discrete Structures and Applications, 2019
    Let $\\mathbb{F}_q$ be a finite field with $q$ elements and $n$ be a positive integer. In this paper, we determine the weight distribution of a class cyclic codes of length $2^n$ over $\\mathbb{F}_q$ whose parity check polynomials are either binomials or trinomials with $2^l$ zeros over $\\mathbb{F}_q$, where integer $l\\ge 1$. In addition, constant weight and two-weight linear codes are constructed when $q\\equiv3\\pmod 4$.
  • Some special cyclic codes of length 2 n
    Manjit Singh, Sudhir Batra
    Journal of Algebra and Its Applications, 2017
    The explicit expressions of generator polynomials of cyclic codes of length [Formula: see text] over finite fields are obtained. The coefficients of these generator polynomials and check polynomials are obtained through modular Lucas sequences. Further, using these polynomials, self-dual, reversible and self-orthogonal cyclic codes of length [Formula: see text] are classified.