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<p>We investigate unbiased weighing matrices of weight 9 and provide a construction method using mutually suitable Latin squares. For <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10623_2025_1676_Article_IEq1.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">\(n \le 16\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>≤</mo> <mn>16</mn> </mrow> </math></EquationSource> </InlineEquation>, we determine the maximum size among sets of mutually unbiased weighing matrices of order <i>n</i> 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.</p>

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Unbiased weighing matrices of weight 9

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月28日

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  • Makoto Araya,
  • Masaaki Harada,
  • Hadi Kharaghani,
  • Sho Suda,
  • Wei-Hsuan Yu

摘要

We investigate unbiased weighing matrices of weight 9 and provide a construction method using mutually suitable Latin squares. For \(n \le 16\) n ≤ 16 , 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.