Unbiased weighing matrices of weight 9
Abstract We investigate unbiased weighing matrices of weight 9 and provide a construction method using mutually suitable Latin squares. For $$n \le 16$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>≤</mml:mo> <mml:mn>16</mml:mn> </mml:mrow> </mml:math> , we determine the maximum size among sets of mutually unbiased weighing matrices of order n and weight 9. Notably, our findings reveal that 13 is the smallest order where such pairs exist, and 16 is the first order for which a maximum class of unbiased weighing matrices is found.
Authors
- Makoto Araya (ORCID: https://orcid.org/0000-0002-9935-038X)
- Hadi Kharaghani (ORCID: https://orcid.org/0000-0003-0115-7117)
- Wenbao Yu (ORCID: https://orcid.org/0000-0001-8860-2644)
- Sho Suda (ORCID: https://orcid.org/0000-0002-5280-2668)
- Masaaki Harada
Institutions
- University of Lethbridge (CA)
- Shizuoka University (JP)
- Tohoku University (JP)
- National Central University (TW)
- National Defense Academy of Japan (JP)
Publication Details
- Journal
- Designs Codes and Cryptography
- Published
- 2025-06-28
- DOI
- https://doi.org/10.1007/s10623-025-01676-y
- Citations
- 1
- Primary Topic
- Coding theory and cryptography
- Type
- article
- Field-Weighted Citation Impact
- 2.48
Funders
- Soochow University
- Natural Sciences and Engineering Research Council of Canada
- Japan Society for the Promotion of Science