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<p>Skew-regular Hadamard matrices are defined for the first time as skew-type Hadamard matrices with constant absolute row-sums. We show at least <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\text {157132}\)</EquationSource> <EquationSource Format="MATHML"><math> <mtext>157132</mtext> </math></EquationSource> </InlineEquation> exist for order <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\text {36}\)</EquationSource> <EquationSource Format="MATHML"><math> <mtext>36</mtext> </math></EquationSource> </InlineEquation>, at least <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\text {2}\)</EquationSource> <EquationSource Format="MATHML"><math> <mtext>2</mtext> </math></EquationSource> </InlineEquation> for order <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\text {100}\)</EquationSource> <EquationSource Format="MATHML"><math> <mtext>100</mtext> </math></EquationSource> </InlineEquation>, and none for order <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(16m^2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>16</mn> <msup> <mi>m</mi> <mn>2</mn> </msup> </mrow> </math></EquationSource> </InlineEquation> where <i>m</i> is a positive integer. These findings have significant implications.</p>

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On skew-regular Hadamard matrices

  • 期刊论文

  • 发表日期：

    2026年1月24日

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  • Hadi Kharaghani,
  • Darcy Best,
  • Sho Suda,
  • Behruz Tayfeh-Rezaie,
  • Vlad Zaitsev

摘要

Skew-regular Hadamard matrices are defined for the first time as skew-type Hadamard matrices with constant absolute row-sums. We show at least \(\text {157132}\) 157132 exist for order \(\text {36}\) 36 , at least \(\text {2}\) 2 for order \(\text {100}\) 100 , and none for order \(16m^2\) 16 m 2 where m is a positive integer. These findings have significant implications.