On Hadamard matrices constructible by circulant submatrices

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.