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<p>Some results have been obtained on the embedding of all 1 matrix <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13226_2025_826_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(J_{n}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>J</mi> <mi>n</mi> </msub> </math></EquationSource> </InlineEquation> of order <i>n</i> into the Hadamard matrix. New theorems on doubling Hadamard matrices have been obtained. Certain methods and conditions have been obtained for embedding the circulant partial Hadamard matrix of row sums 2 and 4 into the Hadamard matrix. A new representation of 4-row regular circulant partial Hadamard matrices has been identified.</p>

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Embedding into Hadamard matrices

  • 期刊论文

  • 发表日期：

    2025年7月6日

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  • Pankaj Kumar Manjhi

摘要

Some results have been obtained on the embedding of all 1 matrix \(J_{n}\) J n of order n into the Hadamard matrix. New theorems on doubling Hadamard matrices have been obtained. Certain methods and conditions have been obtained for embedding the circulant partial Hadamard matrix of row sums 2 and 4 into the Hadamard matrix. A new representation of 4-row regular circulant partial Hadamard matrices has been identified.