Teaching
Teaching
• Modern Algebra
• Advanced Algebra
• Linear Algebra
• Mathematics-II
• Cryptography
• Coding Theory
Designation: Professor
Department: Mathematics & Computing
Email: abhay[at]iitism[dot]ac[dot]in
Contact Number: 8986696177
Office Number: +91-326-223-5670
Personal Page: Under Construction
About Me: Abhay Kumar Singh received a M.Sc. degree in Mathematics from Institute of Science, Banaras Hindu University, Varanasi, India, in 2002, and a PhD degree in Algebra from IIT (BHU) Varanasi, India, in 2007. Currently he is working as a Professor in the Department of Mathematics and Computing, IIT Dhanbad, India. He has been working on the areas of Algebraic Coding theory, Code Base Cryptography. He has also published papers in some highly reputed journals like IEEE Transactions on Information Theory, IEEE Communications Letters, Design Codes and Cryptography, Discrete Mathematics, Theoretical Computer Sciences, Journal of Algebra and Its Applications, Applicable Algebra, Engineering Computing and Communications, etc.
Research Interest: Coding Theory, Post Quantum Cryptography, Quantum Computing
• Modern Algebra
• Advanced Algebra
• Linear Algebra
• Mathematics-II
• Cryptography
• Coding Theory
Ph.D. Indian Institute of Technology (Banaras Hindu University), 2007
Dissertation Topic: ”Characterization of Compressible Modules, Clean Rings and study of the properties of such Modules related with Injectivity”
M.Sc., Mathematics Banaras Hindu University, Varanasi, Uttar Pradesh, India, First Division 2002.
CSIR-JRF (NET) Mathematical Sciences 2005
• CSIR-UGC (NET) Mathematical Sciences 2004
• Graduate Aptitude Test for Engineering(GATE) Mathematics, IIT Madras 2003 (AIR 265)
Professor Department of Mathematics & Computing, Indian Institute of Technology (ISM), Dhanbad, India April 20, 2026- Present
Associate Professor Department of Mathematics & Computing, Indian Institute of Technology (ISM), Dhanbad, India April 12, 2021- April 19, 2026
Visiting Associate Professor Vietnam Institute for Advanced Study in Mathematics, Hanoi, Vietnam May 19, 2022- July 18, 2022
Visiting Associate Professor University of Melbourne, Australia September 01 to September 30, 2023
Visiting Faculty Indian Institute of Management, Rohtak October, 2020- April, 2021
Assistant Professor Indian Institute of Technology (ISM), Dhanbad, July, 2010- April, 2021 September
Assistant Professor Mahatma Gandhi Kashi Vidyapith, Varanasi, India September 2009- June, 2010
Lecturer UIET, CSJM University Kanpur, March, 2007- August, 2009
Guided two Ph. D. students jointly with Prof. Hai Q. Dinh, Kent State University, Ohio, USA.
• Jointly guided an integrated M.Tech student, Vatsal Jha, with Prof. Udaya Parampalli, Melbourne University, Australia on Quantum Coding.
• Offered visiting position in summer 2019 at Telecom Paris Tech, France with monthly stipend 2500 Euro per month.
• Visiting Associate Professor, Vietnam Instiute for Advance Study in Mathematics, Hanoi, May 17, 2022 to July 16, 2022.
• Visiting Associate Professor, Department of CSE, University of Melbourne, Aus tralia. Sept. 1 to Sept. 30, 2023.
Selected Publications:
Orchid id: https://orcid.org/0000-0003-0588-9163
Gyanendra K Verma, Anamika Singh, and Abhay Kumar Singh Function-Correcting b-symbol Codes for Locally (λ, ρ, b)-Functions. IEEE Transactions on Information Theory, Accepted 2025.
Gyanendra K verma, Nupur Patanakar, and Abhay Kumar Singh. CODE SIZE CONSTRAINTS IN b-SYMBOL READ CHANNELS: A BOUND ANALYSIS. IEEE Transactions on Information Theory (2025) ( Accepted).
Pratyush Kumar, Ankur, and Abhay Kumar Singh. Lee Metric Codes Over Symbol-Pair Reed Channels. Discrete Mathematics(Elsevier), 2025 ( Accepted).
Bose, M.K., Parampalli, U. & Abhay Kumar Singh Binary cyclic codes from permutation poly-nomials over F(2)m. Designs, Codes and Cryptography(Springer)(2025).
Hai Q Dinh, Abhay Kumar Singh, Sukhamoy Pattanayak, and Songsak Sriboonchitta. Cyclic DNA codes over the ring F2+uF2+vF2+uvF2+v2F2+uv2F2. Designs, Codes and Cryptography(Springer), 86(7):1451-1467, 2018.
Abhay Kumar Singh and Pramod Kumar Kewat. On cyclic codes over the ring Zp[u]/⟨uk⟩ . Designs, Codes and Cryptography(Springer), 74(1):113, 2015.
Hai Q Dinh, Abhay Kumar Singh, S. Pattanayak, and Songsak Sriboonchitta. Construction of cyclic DNA codes over the ring Z4[u]/⟨u2 −1⟩ based on the deletion distance. Theoretical Computer Science(Elsevier), 773:27-42, 2019. 23.
Narendra Kumar, Siddhartha Siddhiprada Bhoi, and Abhay Kumar Singh. A study of primer design with w-constacyclic shift over F4. Theoretical Computer Science. 960, 113925, 2023.
Hai Q Dinh, Bac T Nguyen, Abhay Kumar Singh, and Songsak Sriboonchitta. Hamming and symbol-pair distances of repeated-root constacyclic codes of prime power lengths over Fpm+ uFpm. IEEE Communications Letters, 22(12):2400-2403, 2018. 24.
Hai Q Dinh, Abhay Kumar Singh, Narendra Kumar, and Songsak Sriboonchitta. On constacyclic codes over Z4[v]/⟨v2 − v⟩ and their Gray images. IEEE Communications Letters, 22(9):1758-1761, 2018. 25.
Hai Q Dinh, Bac Trong Nguyen, Abhay Kumar Singh, and Songsak Sriboonchitta. On the symbol-pair distance of repeated-root constacyclic codes of prime power lengths. IEEE Transactions on Information Theory, 64(4):24172430, 2018. 26.
Hai Q Dinh, Abhay Kumar Singh, Pratyush Kumar, and Songsak Sriboonchitta. On the structure of cyclic codes over the ring Z2s[u]/⟨uk⟩. Discrete Mathematics(Elsevier), 341(8):2243-2275, 2018.
Hai Q Dinh, Abhay Kumar Singh, Sampurna Satpati, and Songsak Sriboonchitta. Sym bol triple distance of repeated root constacyclic codes of prime power lengths. Journal of Algebra and Its Applications(World Scientific), 19(11):2050209, 2020.
Hai Q Dinh, Abhay Kumar Singh, Pratyush Kumar, and Songsak Sriboonchitta. Cyclic codes over the ring GR(pe,m)[u]/⟨uk⟩. Discrete Mathematics(Elsevier), 343(1):111-543, 2020.
Pooja Mishra, Chiranjeev Bhaya, Arup Kumar Pal, and Abhay Kumar Singh. Compressed DNA Coding using Minimum Variance Human Tree. IEEE Communications Letters, 24(8):1602-1606, 2020.
Pooja Mishra, Chiranjeev Bhaya, Arup Kumar Pal, and Abhay Kumar Singh. A novel binary operator for designing medical and natural image cryptosystems. Signal Processing: Image Communication, 98 (2021): 116377.
Narendra Kumar, Siddhartha Siddhiprada Bhoi, Ruchir Gupta and Abhay Kumar Singh. Sliding window symbol-pair constrained codes for energy harvesting, Annals of Telecommunications, 78, pp. 71-77, 2023.
Bhoi, Siddhartha Siddhiprada, Paramapalli Udaya, and Abhay Kumar Singh. ”Construc tion of Multiple Constrained DNA Codes.”Cryptography and Communications Discrete Structures, Boolean Functions and Sequences(Springer) (2024).
V. Pramod Jha, U. Parampalli and Abhay Kumar Singh. Stabilizer codes and Symbol-Pair Metric are Related, IEEE International Symposium on Information Theory (ISIT), pp. 2969-2973, 2022.
Hai Q Dinh, Narendra Kumar and Abhay Kumar Singh. Quantum Codes over non finite chain rings, Cryptography and Communications Discrete Structures, Boolean
Functions and Sequences(Springer), 14, pp. 909-923, 2022.
1. V. Pramod Jha, U. Parampalli and Abhay Kumar Singh. Stabilizer codes and Symbol-Pair Metric are Related, IEEE International Symposium on Information Theory (ISIT), pp. 2969-2973, 2022.
2. Abhay Kumar Singh and Narendra Kumar. Construction of Distance-Optimal Z4-Linear Codes via Cyclic Codes Over a Non-Chain Ring, IEEE International Sympo-
sium on Information Theory (ISIT), 2025 ( Accepted).
3. Bindal, E., Singh, A.K., Singh, M.K. (2025). A Novel PQ-KEM Based on Coding Theory. INDOCRYPT . Lecture Notes in Computer Science, vol 15496. Springer,
Cham. https://doi.org/10.1007/978-3-031-80311-6 13, 2024.
CSS construction with Symbol-pair Metric over Finite Field Metrics funding scheme of Science and Engineering Research Board, Department of Science & Technology Grant Amount: 6.60 Lakhs INR
Ongoing March 2022- March 2025
Design and Analysis of Code-based Public-Key Cryptosystem Defense Research and Development Organisation Grant Amount: 49.892 Lakhs INR
Ongoing July 2022- March 2025
Symbol-Pair Codes over Finite Rings Extramural Research (EMR) funding scheme of Science and Engineering Research Board, Department of Science & Technology Grant Amount: 15.32 Lakhs INR
Completed 2017-2020
Compressible Modules and their Application National Board for Higher Mathematics, Department of Atomic Energy Grant Amount: 3.53 lakhs INR
Characterisation of Clean Rings FRS Scheme, Indian Institute of Technology (ISM), Dhanbad Grant Amount: 3.90 Lakhs INR
Completed 2010-2013