Some new series of Hadamard matrices
We show that the following theorems hold: Theorem 1. If \(q\equiv 1\) (mod 8) is a prime power and there exists a Hadamard matrix of order (q-1)/2, then we can construct a Hadamard matrix of order 4q. Theorem 2. If \(q\equiv 5\) (mod 8) is a prime power and there exists a skew-Hadamard matrix of order \((q+3)/2\), then we can construct a Hadamard matrix of order \(4(q+2).\) Theorem 3. If \(q\equiv 1\) (mod 8) is a prime power and there exists a symmetric C-matrix of order \((q+3)/2\), then we can construct a Hadamard matrix of order \(4(q+2)\).
scientific article; zbMATH DE number 4079443