Classification of Hadamard matrices of order 28 (Q1336695)

As usual, an Hadamard matrix \(H\) of order \(n\) is an \(n\times n\) matrix of 1's and \(-1\)'s with \(HH^ T= nI\). In some earlier works [On equivalence of Hadamard matrices, Hokkaido Math. J. 17, No. 1, 139-146 (1988; Zbl 0694.05018); Hadamard matrices of order 28, Mem. Fac. Ed. Ehime Univ. Natur. Sci. 7, 7-57 (1987)], the author constructed all inequivalent Hadamard matrices with Hall sets of order 28 and classified by \(K\)- matrices associated with Hadamard matrices except five matrices. In this paper, the author proved that Hadamard matrices with the trivial \(K\)-matrix are equivalent to the Paley matrix defined by the squares in GF(27). By this theorem, the author got a complete classification of Hadamard matrices of order 28, and had inequivalent Hadamard matrices of order 28.