Ring theory applications in coding and error detection
*Narayan NaikCorresponding authornarayan.naik@canaraengineering.inDepartment of Information Science & Engineering Canara Engineering College VTU Canara Engineering College Sudheendra Nagar, Benjanapadavu Bantwal Taluk D.K. DistrictMangalore, Karnataka, 574219, IndiaView full profile → , Suman M9sumanm@gmail.comDepartment of Artificial Intelligence and Data Science B.M.S College of EngineeringBangalore, Karnatka, 560019, IndiaView full profile → , Rajeshwari. Nrajeshwarin@bit-bangalore.edu.inDepartment of MCA Bangalore Institute of Technology K. R. Road,V. V. PuraBengaluru, Karnatka, 560004, IndiaView full profile → , Murigendrayya M Hiremathmmh.eda@gmail.comDepartment of Medical Electronics Engineering Dayananda Sagar College of Engineering Kumaraswamy LayoutBangalore, Karantaka, 560111, IndiaView full profile → , Gangadhar T Ggangadhar-air@dsu.edu.inDepartment of Artificial Intelligence and Robotics Dayananda Sagar University DevarakaggalahalliHoraohalli, Karnataka, 562112, IndiaView full profile → , Shalini M Gshalini-ece@dsatm.edu.inDepartment of Electronics and Communication Engineering Dayananda Sagar Academy of Technology and ManagementBangalore, Karnataka, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 08 Jul 2025
- Published Online:
- 31 Oct 2025
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-2561
- Pages:
- 2907–2914
Abstract
Keywords
Subject Classifications
References
[1] A. Alahmadi, T. Alihia, R. A. Betty, L. Galvez, and P. Solé, “The build-up construction for codes over a commutative non-unitary ring of order 9,” Mathematics, vol. 12, pp. 860 (2024).
[2] A. Alahmadi, T. Alihia, and P. Solé, “The build-up construction for codes over a non-commutative non-unitary ring of order 9,” AIMS Math., vol. 9, pp. 18278-18307 (2024).
[3] N. Gassner, M. Greferath, J. Rosenthal, and V. Weger, “Bounds for coding theory over rings,” Entropy, vol. 24, pp. 1473 (2022), doi: 10.3390/e24101473.
[4] C. Xie, H. Chen, C. Li, and S. Mesnager, “Constructions of self-orthogonal linear codes and dual-containing BCH codes,” IEEE Trans. Inf. Theory, vol. 71, pp. 5049-5062 (2025).
[5] S. M. Stefanov, “On the solution of two-person zero-sum matrix games,” J. Inf. Optim. Sci., vol. 45, no. 3, pp. 649-657 (2024), doi: 10.47974/JIOS-1323.
[6] A. Lemoine, R. Mora, and J. P. Tillich, “Understanding the new distinguisher of alternant codes at degree 2,” Des. Codes Cryptogr., pp. 1-23 (2025).
[7] S. Sylviani, N. Anastasya, E. Carnia, F. C. Permana, and N. Anggriani, “Algebraic approaches to information security: Applying ring matrix groups for enhanced protection,” Appl. Math. Inf. Sci., vol. 19, no. 3, pp. 725-738 (May 2025), doi: 10.18576/amis/190320.
[8] N. Tang, Y. S. Han, D. Pei, and C. Chen, “A fast decoding algorithm for generalized Reed-Solomon codes and alternant codes,” arXiv:2502.02356 (2025).
[9] M. Sajjad, T. Shah, M. Abbas, M. Alammari, and R. J. Serna, “The impact of alternant codes over Eisenstein integers on modern technology,” Comput. Appl. Math., vol. 44, pp. 95 (2025).
[10] M. N. B. V. Thorat, “Seismic behavior of composite steel-concrete beams in high-risk earthquake zones: An analytical and experimental approach,” IJRAET, vol. 14, no. 2, pp. 11-18 (Aug. 2025).
[11] J. Bariffi, H. Bartz, G. Liva, and J. Rosenthal, “Error-correction performance of regular ring-linear LDPC codes over Lee channels,” IEEE Trans. Inf. Theory, vol. 70, no. 11, pp. 7820-7839 (Nov. 2024), doi: 10.1109/TIT.2024.3436938.




