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Mathematics of Computation

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On Hadamard matrices constructible by circulant submatrices

Author: C. H. Yang
Journal: Math. Comp. 25 (1971), 181-186
MSC: Primary 05.25
Corrigendum: Math. Comp. 28 (1974), 1183-1184.
Corrigendum: Math. Comp. 28 (1974), 1183-1184.
MathSciNet review: 0288037
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Abstract: Let ${V_{2n}}$ be an H-matrix of order 2n constructible by using circulant $n \times n$ submatrices. A recursive method has been found to construct ${V_{4n}}$ by using circulant $2n \times 2n$ submatrices which are derived from $n \times n$ submatrices of a given ${V_{2n}}$. A similar method can be applied to a given ${W_{4n}}$, an H-matrix of Williamson type with odd n, to construct ${W_{8n}}$. All ${V_{2n}}$ constructible by the standard type, for $1 \leqq n \leqq 16$, and some ${V_{2n}}$, for $n \geqq 20$, are listed and classified by this method.

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Keywords: Construction of Hadamard matrices, circulant matrices, standard type <I>H</I>-matrices, Williamson type <I>H</I>-matrices, recursive method for <I>H</I>-matrices, table for some <I>H</I>-matrices
Article copyright: © Copyright 1971 American Mathematical Society