A new class of Hadamard matrices

Abstract

A Hadamard matrixHis an orthogonal square matrix of ordermall the entries of which are either + 1 or - 1; i. e. whereH′denotes the transpose ofHandI_mis the identity matrix of orderm. For such a matrix to exist it is necessary [1] that It has been conjectured, but not yet proved, that this condition is also sufficient. However, many values ofmhave been found for which a Hadamard matrix of ordermcan be constructed. The following is a list of suchm(pdenotes an odd prime).