A new symmetric weighing matrix SW(22,16)

Sheet Nihal Topno and Shyam Saurabh
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 31, 2025, Number 3, Pages 443–447
DOI: 10.7546/nntdm.2025.31.3.443-447
Full paper (PDF, 180 Kb)

Details

Authors and affiliations

Sheet Nihal Topno
University Department of Mathematics, Ranchi University
Ranchi, Jharkhand, India

Shyam Saurabh
Department of Mathematics, Tata College, Kolhan University
Chaibasa, Jharkhand, India

Abstract

The existence of symmetric weighing matrix is settled in this note through a theorem and exhaustive search.

Keywords

• Symmetric weighing matrix
• Type 1 matrix

2020 Mathematics Subject Classification

• 05B15
• 05B20

References

1. Ben-Av, R., & Dula, G., Goldberger, A., Kotsireas, I., & Strassler, Y. (2024). New weighing matrices via partitioned group actions. Discrete Mathematics, 347(5), Article ID 113908.
2. Chan, H. C., Rodger, C. A., & Seberry, J. (1986). On inequivalent weighing matrices. Ars Combinatoria, 21-A, 299–333.
3. Craigen, R. & Kharaghani, H. (2007). Orthogonal designs. In: Colbourn, C. J., & Dinitz, J. H. (Eds.). Handbook of Combinatorial Designs (2nd ed.). Chapman & Hall/CRC, Boca Raton, FL, pp. 280–295.
4. Georgiou, S. D., Stylianou, S. & Alrweili, H. (2023). On symmetric weighing matrices. Mathematics, 11(9), Article ID 2076.
5. Paley, R. E. A. C. (1933). On orthogonal matrices. Journal of Mathematical Physics, 12(1–4), 311–320.
6. Seberry, J. (2017). Orthogonal Designs: Hadamard Matrices, Quadratic Forms and Algebras. Springer International Publishing AG.

Manuscript history

• Received: 18 October 2024
• Revised: 2 June 2025
• Accepted: 24 July 2025
• Online First: 28 July 2025

Copyright information

Ⓒ 2025 by the Authors.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).