On inequivalent Hadamard Matrices of Order \(44\)

Abstract

In this paper, we construct many Hadamard matrices of order \(44\) and we use a new efficient algorithm to investigate the lower bound of inequivalent Hadamard matrices of order \(44\). Using four \((1, -1)\)-circulant matrices of order \(11\) in the Goethals-Seidel array, we obtain many new Hadamard matrices of order \(44\) and we show that there are at least \(6018\) inequivalent Hadamard matrices for this order. Moreover, we use a known method to investigate the existence of double even self-dual codes \([88, 44, d]\) over \(\text{GF}(2)\) constructed from these Hadamard matrices.