An infinite family of Hadamard matrices constructed from Paley type matrices

Abstract

An n x n matrix whose entries are from the set {1,-1} is called a Hadamard matrix if HH? = nIn. The Hadamard conjecture states that if n is a multiple of four then there always exists Hadamard matrices of this order. But their construction remain unknown for many orders. In this paper we construct Hadamard matrices of order 2q(q + 1) from known Hadamard matrices of order 2(q + 1), where q is a power of a prime number congruent to 1 modulo 4. We show then two ways to construct them. This work is a continuation of U. Scarpis? in [7] and Dragomir-Z. Dokovic?s in [10].