Bodigiri Sai Gopinadh

@gmrit.edu.in

Assistant Professor and Department of Mathematics
GMR Institute of Technology

Bodigiri Sai Gopinadh


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https://researchid.co/saigopinadh

RESEARCH, TEACHING, or OTHER INTERESTS

Algebra and Number Theory, Computer Science Applications
7

Scopus Publications

15

Scholar Citations

1

Scholar h-index

1

Scholar i10-index

Scopus Publications

  • Reversible Codes in Matn×s(Fq) Under NRT-Metric
    Bodigiri Sai Gopinadh, Venkatrajam Marka
    IEEE Access, 2025
    Reversible codes play an essential role in coding theory because of their structural symmetry and broad applications in error control, cryptography, and DNA computing. This study investigates reversible codes over the matrix space <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Mat<sub>n×s</sub></i>(F<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>q</i></sub>) equipped with the Niederreiter–Rosenbloom–Tsfasman (NRT) metric. We introduce the concepts of reversible and self-reversible codes in the NRT-metric and establish several structural properties of these codes. Explicit conditions for the reversibility of linear codes based on generator matrices were derived for both the even and odd dimensions. We further prove that the duals of NRT-reversible codes are also NRT-reversible and present characterizations linking the number of self-reversible codewords with the block structure of generator matrices. The necessary and sufficient condition for a self-dual code to be reversible is proven for both the even and odd dimensions. Several examples of codes over finite fields illustrate and demonstrate the construction of NRT-reversible codes.
  • RT-conjugate codes in the Rosenbloom-Tsfasman metric
    Bodigiri Sai Gopinadh, Venkatrajam Marka
    Boletim Da Sociedade Paranaense De Matematica, 2025
    Linear Complementary Dual (LCD) codes are a special class of linear error-correcting code used in data transmission and storage. These codes possess specific algebraic properties that make them useful in applications, such as communication systems, cryptography, and data storage devices. These are particularly valuable in scenarios that require a high degree of error detection and correction. This study explores the characteristics of RT-conjugate codes within the Rosenbloom-Tsfasman metric (RT-metric). In this study, we focus on a specific subclass of LCD codes characterized by conjugate conditions. In particular, we establish sufficient conditions under which a linear code in the RT metric qualifies as an LCD code through its conjugate structure. We also analyzed the weight distribution of the dual of these codes in terms of their type and proposed several construction methods for RT-conjugate codes.
  • Construction of reversible MDS codes in the Rosenbloom-Tsfasman metric
    Bodigiri Sai Gopinadh,, Venkatrajam Marka
    Aims Mathematics, 2025
    Maximum distance separable (MDS) codes are a type of error-correcting codes that aim to optimize the shortest possible distance between codewords. These codes are useful in situations where error correction is critical, such as data storage or communication systems, and they can be found in a variety of domains, including information theory, cryptography, and reliable data transmission. The concept of MDS codes is fundamental in designing robust and efficient error-correcting codes that can withstand the challenges posed by noisy communication channels or unreliable storage systems. The Rosenbloom-Tsfasman (RT) metric provides a framework for constructing codes optimized for error correction, and reversible codes leverage this to maximize their error-correction capabilities. This study explored the characteristics of reversible MDS codes in the RT-metric by analyzing the structure of different types of generator matrices. It also established various properties of these codes, such as the conditions under which certain reversible MDS codes were self-dual over $ \mathbb{F}_2 $ and $ \mathbb{F}_q $. In addition, this study proposed several constructions for reversible MDS codes in the RT-metric.
  • Reversible codes in the Rosenbloom-Tsfasman metric
    Bodigiri Sai Gopinadh, Venkatrajam Marka
    Aims Mathematics, 2024
    &lt;p&gt;Reversible codes have a range of wide applications in cryptography, data storage, and communication systems. In this paper, we investigated reversible codes under the Rosenbloom-Tsfasman metric (RT-metric). First, some properties of reversible codes in the RT-metric were described. An essential condition for a reversible code to be a maximum distance separable code (MDS code, in short) in the RT-metric was established. A necessary condition for a binary self-dual code to be reversible was proven and the same was generalized for $ q $-ary self-dual reversible codes. Several constructions for reversible RT-metric codes were provided in terms of their generator matrices.&lt;/p&gt;
  • Strange Chaotic Attractors and Existence Results via Nonlinear Fractional Order Systems and Fixed Points
    Sumati Kumari Panda, Velusamy Vijayakumar, Bodigiri Sai Gopinadh, Fahd Jarad
    Industrial and Applied Mathematics, 2024
  • Revisiting Darbo’s Fixed Point Theory with Application to a Class of Fractional Integral Equations
    Rahul, Nihar Kumar Mahato, Bodigiri Sai Gopinadh, Sumati Kumari Panda
    Industrial and Applied Mathematics, 2024
  • Codes in rosenbloom-tsfasman metric: A survey
    Bodigiri Sai Gopinadh, Venkatrajam Marka
    Journal of Physics Conference Series, 2021
    This paper gives a systematic survey of research carried out in the theory of codes equipped with Rosenbloom-Tsfasman metric. In classical coding theory setting, codes are investigated with respect to the Hamming metric which can efficiently address the communication problems arising from channels in which channel noise generates equiprobable errors. But however, not all the real world channels are of that nature, especially, when the possible errors form patterns of a specific shape. Rosenbloom and Tsfasman introduced a non-Hamming metric, called Rosenbloom-Tsfasman metric (RT-metric, in short) that can address the problem of reliable information transmission over parallel noisy channels. Martin, Stinson and Skriganov independently introduced the same metric in the context of the theory of uniform distributions. As this metric happened to be a generalization of the classical Hamming metric, it has attracted so much attention from the coding theory research community and as a result a lot of work has been done in this line of research over the past 3 decades. In this paper we would like to present the key developments in the field of codes with RT-metric.

RECENT SCHOLAR PUBLICATIONS

  • Reversible codes over Mat n×s (F q ) in NRT-metric
    BS Gopinadh, V Marka
    IEEE Access , 2025
    2025.0
  • RT-conjugate codes in Rosenbloom-Tsfasman metric
    BS Gopinadh, V Marka
    Boletim da Sociedade Paranaense de Matemática 43 (4) , 2025
    2025.0
  • Reversible Codes in Mat n×s (Fq) Under NRT-Metric
    BS Gopinadh, V Marka
    IEEE Access 13, 197414-197424 , 2025
    2025.0
  • Construction of reversible MDS codes in the Rosenbloom-Tsfasman metric
    BS Gopinadh, V Marka
    AIMS Mathematics 10 (10), 24240-24256 , 2025
    2025.0
  • Strange Chaotic Attractors and Existence Results via Nonlinear Fractional Order Systems and Fixed Points
    SK Panda, V Vijayakumar, BS Gopinadh, F Jarad
    Recent Developments in Fixed-Point Theory: Theoretical Foundations and Real … , 2024
    2024.0
  • Revisiting Darbo’s Fixed Point Theory with Application to a Class of Fractional Integral Equations
    Rahul, N Kumar Mahato, B Sai Gopinadh, SK Panda
    Recent Developments in Fixed-Point Theory: Theoretical Foundations and Real … , 2024
    2024.0
  • Recent developments in fixed-point theory: Theoretical foundations and real-world applications
    M Younis, L Chen, D Singh
    Springer , 2024
    2024.0
    Citations: 11
  • Connecting nonlinear -contractions and fractional operators in the modelling of novel Coronavirus 2019-nCoV/SARS-CoV-2
    B HAZARIKA, S Panda, V VIJAYAKUMAR, B Gopinadh
    authorea , 2024
    2024.0
  • Connecting nonlinear -contractions and fractional operators in the modelling of novel Coronavirus 2019-nCoV/SARS-CoV-2
    B HAZARIKA, S Panda, V VIJAYAKUMAR, B Gopinadh
    2024.0
  • Connecting nonlinear (\varpi-F_ {{C}})-contractions and fractional operators in the modelling of novel Coronavirus 2019-nCoV/SARS-CoV-2
    B Hazarika, S Panda, V Vijayakumar, B Gopinadh
    ESS Open Archive eprints 573, 57396372 , 2024
    2024.0
  • Reversible codes in the Rosenbloom-Tsfasman metric
    BS Gopinadh, V Marka
    AIMS Mathematics 9 (8), 22927-22940 , 2024
    2024.0
    Citations: 1
  • Codes in Rosenbloom-Tsfasman metric: A Survey
    BS Gopinadh, V Marka
    Journal of Physics: Conference Series 1770 (1), 012090 , 2021
    2021.0
    Citations: 1
  • GENERALISED RELATION AMONG UPPER BOUNDS IN A SPECIAL CASE BY TAYLOR’S SERIES
    BSAIG NADH, NV MADDULURI
    Acta Ciencia Indica 41 (No. 4,), 277 (2015) , 2015
    2015.0
  • An Inductive Attempt to Prove Mean Value Theorem for n-Real Valued Functions
    KVL Narasimhacharyulu, BSG Nadh
    2013.0
    Citations: 1
  • Recent Developments in Fixed-Point Theory
    M Younis, L Chen, D Singh
    Springer , 0
    Citations: 1

MOST CITED SCHOLAR PUBLICATIONS

  • Recent developments in fixed-point theory: Theoretical foundations and real-world applications
    M Younis, L Chen, D Singh
    Springer , 2024
    2024.0
    Citations: 11
  • Reversible codes in the Rosenbloom-Tsfasman metric
    BS Gopinadh, V Marka
    AIMS Mathematics 9 (8), 22927-22940 , 2024
    2024.0
    Citations: 1
  • Codes in Rosenbloom-Tsfasman metric: A Survey
    BS Gopinadh, V Marka
    Journal of Physics: Conference Series 1770 (1), 012090 , 2021
    2021.0
    Citations: 1
  • An Inductive Attempt to Prove Mean Value Theorem for n-Real Valued Functions
    KVL Narasimhacharyulu, BSG Nadh
    2013.0
    Citations: 1
  • Recent Developments in Fixed-Point Theory
    M Younis, L Chen, D Singh
    Springer , 0
    Citations: 1
  • Reversible codes over Mat n×s (F q ) in NRT-metric
    BS Gopinadh, V Marka
    IEEE Access , 2025
    2025.0
  • RT-conjugate codes in Rosenbloom-Tsfasman metric
    BS Gopinadh, V Marka
    Boletim da Sociedade Paranaense de Matemática 43 (4) , 2025
    2025.0
  • Reversible Codes in Mat n×s (Fq) Under NRT-Metric
    BS Gopinadh, V Marka
    IEEE Access 13, 197414-197424 , 2025
    2025.0
  • Construction of reversible MDS codes in the Rosenbloom-Tsfasman metric
    BS Gopinadh, V Marka
    AIMS Mathematics 10 (10), 24240-24256 , 2025
    2025.0
  • Strange Chaotic Attractors and Existence Results via Nonlinear Fractional Order Systems and Fixed Points
    SK Panda, V Vijayakumar, BS Gopinadh, F Jarad
    Recent Developments in Fixed-Point Theory: Theoretical Foundations and Real … , 2024
    2024.0
  • Revisiting Darbo’s Fixed Point Theory with Application to a Class of Fractional Integral Equations
    Rahul, N Kumar Mahato, B Sai Gopinadh, SK Panda
    Recent Developments in Fixed-Point Theory: Theoretical Foundations and Real … , 2024
    2024.0
  • Connecting nonlinear -contractions and fractional operators in the modelling of novel Coronavirus 2019-nCoV/SARS-CoV-2
    B HAZARIKA, S Panda, V VIJAYAKUMAR, B Gopinadh
    authorea , 2024
    2024.0
  • Connecting nonlinear -contractions and fractional operators in the modelling of novel Coronavirus 2019-nCoV/SARS-CoV-2
    B HAZARIKA, S Panda, V VIJAYAKUMAR, B Gopinadh
    2024.0
  • Connecting nonlinear (\varpi-F_ {{C}})-contractions and fractional operators in the modelling of novel Coronavirus 2019-nCoV/SARS-CoV-2
    B Hazarika, S Panda, V Vijayakumar, B Gopinadh
    ESS Open Archive eprints 573, 57396372 , 2024
    2024.0
  • GENERALISED RELATION AMONG UPPER BOUNDS IN A SPECIAL CASE BY TAYLOR’S SERIES
    BSAIG NADH, NV MADDULURI
    Acta Ciencia Indica 41 (No. 4,), 277 (2015) , 2015
    2015.0