Construction of generalized Hadamard matrices \(D(r^m(r+1),r^m(r+1);p)\)
A difference matrix \(D(\lambda p,m;p)\) is a \(\lambda p \times m\) matrix, with entries in \(G\), where \(G\) is a finite abelian group of order \(p\), such that the vector difference of any two columns contains each element of \(G\) \(\lambda \) times. A generalized Hadamard matrix is a difference matrix with \(\lambda p =m.\) The authors give a method for constructing generalized Hadamard matrices \(D(r^m(r+1),r^m(r+1);p)\) for \(n \geq 1\) from known \(D(r,r;r)\) and \(D(r+1,r+1;p)\) generalized Hadamard matrices. The orthogonal arrays \(L_{r^m(r+1)_p}((r^m(r+1))^1p^{r^m(r+1)})\) are equivalent to these constructed Hadamard matrices. These structures are then used to construct other difference matrices and orthogonal arrays using orthogonal decomposition of projection matrices.
scientific article; zbMATH DE number 1790178
scientific article